Fatoring polinomials - 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.