Why does $9x(x − 1) = 9x − 5$ imply $9x^2 − 18x + 5 = 0$? [closed]

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Define
$$f(x) = 9x(x - 1) quadtextandquad g(x) = 9x - 5$$
We have
$$
begin align
f(x)=g(x)&implies 9x(x − 1) = 9x − 5 \
&implies 9x^2 − 18x + 5 = 0 \
&implies (3x)^2 − 6(3x) + 5 = 0 \
&implies (3x − 1)(3x − 5) = 0
endalign
$$

Can someone tell me here, why the $9x(x - 1) = 9x - 5$
leads to $9x^2 - 18x + 5 = 0$?

algebra-precalculus

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edited Jul 30 at 0:52

Crosby

341117

asked Jul 30 at 0:14

Bernie Sanders

12

closed as off-topic by user223391, Xander Henderson, John Ma, Extremal, Key Flex Jul 30 at 1:22

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Xander Henderson, John Ma, Key Flex

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

up vote
-1
down vote

favorite

Define
$$f(x) = 9x(x - 1) quadtextandquad g(x) = 9x - 5$$
We have
$$
begin align
f(x)=g(x)&implies 9x(x − 1) = 9x − 5 \
&implies 9x^2 − 18x + 5 = 0 \
&implies (3x)^2 − 6(3x) + 5 = 0 \
&implies (3x − 1)(3x − 5) = 0
endalign
$$

Can someone tell me here, why the $9x(x - 1) = 9x - 5$
leads to $9x^2 - 18x + 5 = 0$?

algebra-precalculus

share|cite|improve this question

edited Jul 30 at 0:52

Crosby

341117

asked Jul 30 at 0:14

Bernie Sanders

12

closed as off-topic by user223391, Xander Henderson, John Ma, Extremal, Key Flex Jul 30 at 1:22

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Xander Henderson, John Ma, Key Flex

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

up vote
-1
down vote

favorite

up vote
-1
down vote

favorite

Define
$$f(x) = 9x(x - 1) quadtextandquad g(x) = 9x - 5$$
We have
$$
begin align
f(x)=g(x)&implies 9x(x − 1) = 9x − 5 \
&implies 9x^2 − 18x + 5 = 0 \
&implies (3x)^2 − 6(3x) + 5 = 0 \
&implies (3x − 1)(3x − 5) = 0
endalign
$$

Can someone tell me here, why the $9x(x - 1) = 9x - 5$
leads to $9x^2 - 18x + 5 = 0$?

algebra-precalculus

share|cite|improve this question

edited Jul 30 at 0:52

Crosby

341117

asked Jul 30 at 0:14

Bernie Sanders

12

Define
$$f(x) = 9x(x - 1) quadtextandquad g(x) = 9x - 5$$
We have
$$
begin align
f(x)=g(x)&implies 9x(x − 1) = 9x − 5 \
&implies 9x^2 − 18x + 5 = 0 \
&implies (3x)^2 − 6(3x) + 5 = 0 \
&implies (3x − 1)(3x − 5) = 0
endalign
$$

Can someone tell me here, why the $9x(x - 1) = 9x - 5$
leads to $9x^2 - 18x + 5 = 0$?

algebra-precalculus

share|cite|improve this question

edited Jul 30 at 0:52

Crosby

341117

asked Jul 30 at 0:14

Bernie Sanders

12

share|cite|improve this question

share|cite|improve this question

edited Jul 30 at 0:52

Crosby

341117

edited Jul 30 at 0:52

Crosby

341117

edited Jul 30 at 0:52

Crosby

341117

341117

asked Jul 30 at 0:14

Bernie Sanders

12

asked Jul 30 at 0:14

Bernie Sanders

12

asked Jul 30 at 0:14

Bernie Sanders

12

12

closed as off-topic by user223391, Xander Henderson, John Ma, Extremal, Key Flex Jul 30 at 1:22

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Xander Henderson, John Ma, Key Flex

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by user223391, Xander Henderson, John Ma, Extremal, Key Flex Jul 30 at 1:22

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Xander Henderson, John Ma, Key Flex

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

add a comment | 

1 Answer
1

active

oldest

votes

up vote
6
down vote

From $$9x(x-1)=9x-5$$ applying distributivity of the multiplication with respect to the addition we get $$9x^2-9x=9x-5$$

Adding $-9x+5$ on both sides we get $$9x^2-9x-9x+5=0$$
Associating terms $$9x^2-18x+5=0$$

share|cite|improve this answer

edited Jul 30 at 0:19

Isham

10.5k3829

answered Jul 30 at 0:17

user580373

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I think it might be slightly confusing to use terms such as "distributivity" to someone with this level of algebraic knowledge, without explaining them. But if the OP is still confused: dummies.com/education/math/algebra/…
  – Jam
  Jul 30 at 0:30
  

  
  
  
  

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
6
down vote

From $$9x(x-1)=9x-5$$ applying distributivity of the multiplication with respect to the addition we get $$9x^2-9x=9x-5$$

Adding $-9x+5$ on both sides we get $$9x^2-9x-9x+5=0$$
Associating terms $$9x^2-18x+5=0$$

share|cite|improve this answer

edited Jul 30 at 0:19

Isham

10.5k3829

answered Jul 30 at 0:17

user580373

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I think it might be slightly confusing to use terms such as "distributivity" to someone with this level of algebraic knowledge, without explaining them. But if the OP is still confused: dummies.com/education/math/algebra/…
  – Jam
  Jul 30 at 0:30
  

  
  
  
  

add a comment | 

up vote
6
down vote

From $$9x(x-1)=9x-5$$ applying distributivity of the multiplication with respect to the addition we get $$9x^2-9x=9x-5$$

Adding $-9x+5$ on both sides we get $$9x^2-9x-9x+5=0$$
Associating terms $$9x^2-18x+5=0$$

share|cite|improve this answer

edited Jul 30 at 0:19

Isham

10.5k3829

answered Jul 30 at 0:17

user580373

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I think it might be slightly confusing to use terms such as "distributivity" to someone with this level of algebraic knowledge, without explaining them. But if the OP is still confused: dummies.com/education/math/algebra/…
  – Jam
  Jul 30 at 0:30
  

  
  
  
  

add a comment | 

up vote
6
down vote

up vote
6
down vote

From $$9x(x-1)=9x-5$$ applying distributivity of the multiplication with respect to the addition we get $$9x^2-9x=9x-5$$

Adding $-9x+5$ on both sides we get $$9x^2-9x-9x+5=0$$
Associating terms $$9x^2-18x+5=0$$

share|cite|improve this answer

edited Jul 30 at 0:19

Isham

10.5k3829

answered Jul 30 at 0:17

user580373

From $$9x(x-1)=9x-5$$ applying distributivity of the multiplication with respect to the addition we get $$9x^2-9x=9x-5$$

Adding $-9x+5$ on both sides we get $$9x^2-9x-9x+5=0$$
Associating terms $$9x^2-18x+5=0$$

share|cite|improve this answer

edited Jul 30 at 0:19

Isham

10.5k3829

answered Jul 30 at 0:17

user580373

share|cite|improve this answer

share|cite|improve this answer

edited Jul 30 at 0:19

Isham

10.5k3829

edited Jul 30 at 0:19

Isham

10.5k3829

edited Jul 30 at 0:19

Isham

10.5k3829

10.5k3829

answered Jul 30 at 0:17

user580373

answered Jul 30 at 0:17

user580373

answered Jul 30 at 0:17

user580373

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I think it might be slightly confusing to use terms such as "distributivity" to someone with this level of algebraic knowledge, without explaining them. But if the OP is still confused: dummies.com/education/math/algebra/…
  – Jam
  Jul 30 at 0:30
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I think it might be slightly confusing to use terms such as "distributivity" to someone with this level of algebraic knowledge, without explaining them. But if the OP is still confused: dummies.com/education/math/algebra/…
  – Jam
  Jul 30 at 0:30
  

  
  
  
  

I think it might be slightly confusing to use terms such as "distributivity" to someone with this level of algebraic knowledge, without explaining them. But if the OP is still confused: dummies.com/education/math/algebra/…
– Jam
Jul 30 at 0:30

I think it might be slightly confusing to use terms such as "distributivity" to someone with this level of algebraic knowledge, without explaining them. But if the OP is still confused: dummies.com/education/math/algebra/…
– Jam
Jul 30 at 0:30

add a comment |