Answer
$(2x-1)(3x+2)$
Work Step by Step
Factor using the AC-method.
With $a=6$ and $c=-2$, then $ac=6(-2)=-12$.
Looking for factors of $-12$ whose sum is equal to the middle term's coefficient, which is $1$, gives $4$ and $-3$.
Rewrite the middle term using the factors found to obtain:
\begin{align*}
6x^2+x-2&=6x^2-3x+4x-2
\end{align*}
Factor by grouping to obtain:
\begin{align*}
6x^2+x-2&=(6x^2-3x)+(4x-2)\\
&=3x(2x-1)+2(2x-1)\\
&=(2x-1)(3x+2)
\end{align*}
