Answer
$(2x-1)(3x+2)$
Work Step by Step
We have a quadratic expression $ax^2+bx+c=6x^2+x-2$.
We have: $a=6$ and $c=-2$, then $ac=6(-2)=-12$.
Look for factors of $-12$ whose sum is equal to the middle term's coefficient, which is $1$, and use these factors to rewrite the middle term.
The factors of $-12$ whose sum are $4$ and $-3$.
Rewrite the middle term using these factors and factor by groupingto obtain:
$6x^2+x-2\\
=6x^2-3x+4x-2 \\
=(6x^2-3x)+(4x-2)\\ = 3x(2x-1)+2(2x-1)\\
=(2x-1)(3x+2)$
