How do you factor 3x^2+7x-6=0 and solve?

Do the factoring method
(3x-2)(x+3)
3x=2     X=-3
x=2/3

if we check
3x2+7x=6
3(2/3)2+7(2/3)=6
4/3+14/3=6
18/3=6
The x=2/3 is correct now lets see the x=-3
3x2+7x=6
3(-3)2+7(-3)=6
3(9)-21=6
27-21=6
6=6

so both x can be used in factoring