Answer
$(3y-2)(8y+3)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression
\begin{align*}
24y^2-7y-6
\end{align*} has $ac=
24(-6)=-144
$ and $b=
-7
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-16,9
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
24y^2-16y+9y-6
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(24y^2-16y)+(9y-6)
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
8y(3y-2)+3(3y-2)
.\end{align*}
Factoring the $GCF=
(3y-2)
$ of the entire expression above results to
\begin{align*}
(3y-2)(8y+3)
.\end{align*}
