Answer
$(x-2)(7x+6)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression,
\begin{align*}
7x^2-8x-12
\end{align*}
has $ac=
7(-12)=-84
$ and $b=
-8
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-14,6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
7x^2-14x+6x-12
\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(7x^2-14x)+(6x-12)
\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
7x(x-2)+6(x-2)
\end{align*}
Factoring the $GCF=
(x-2)
$ of the entire expression above results to
\begin{align*}
(x-2)(7x+6)
\end{align*}