Math Help - Fatoring polynomials - what am I doing wrong?

Hi! Here is the problem I was trying to solve, and what I did:

3x^2+7x-6=0
Since 3*(-6)=-18, I need two numbrers, the product of which is -18, and the sum of which is 7. I chose -9 and 2.
3x^2-9x+2x-6=0
3x(x-3)+2(x-3)=0
(3x+2)(x-3)=0
3x+2=0 or x-3=0
x=3 x=-2/3


However, the back of the textbook gives the answer x=-3 x=2/3
What is wrong? Thanks if you could help, big time! I didn't do grade 10 math, and in grade 11 they only review factoring for a couple of lessons.

P.S. Sorry for doubleposting!!

I see it like this

. But does...