6-7u=3u^2
step 1: -3u^2-7u+6=0
step 2: -(3u^2+7u-6)=0
step 3: (3u-2)(u+3)=0 (Answer in the book)

My Question:
In step 3: Why didn't we use 1 and 6 (for 6's Greatest Common Factor) which will result in 7 (linear term). 2 and 3 either give 5 or 1.

Please clarify I'm confused?

Question

6-7u=3u^2
step 1: -3u^2-7u+6=0
step 2: -(3u^2+7u-6)=0
step 3: (3u-2)(u+3)=0 (Answer in the book)

My Question:
In step 3: Why didn't we use 1 and 6 (for 6's Greatest Common Factor) which will result in 7 (linear term). 2 and 3 either give 5 or 1. 

Please clarify I'm confused?

luigi0210 · Answer

Because you're also distributing that $3u$

anonymous · Answer

Oh ok. How could I have missed that. Thank you!

anonymous · Answer

So I just use a different GCF it's not random?

mathstudent55 · Answer

$3u^2 + 7u - 6 $

$ = 3u^2 -2u + 9u - 6$

$=u(3u - 2) +3(3u - 2) $

$=(3u - 2)(u + 3) $