Answer
$(2x-3)(x-12)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression,
\begin{align*}
2x^2-27x+36
\end{align*}
has $ac=
2(36)=72
$ and $b=
-27
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-3,-24
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
2x^2-3x-24x+36
\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(2x^2-3x)-(24x-36)
\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
x(2x-3)-12(2x-3)
\end{align*}
Factoring the $GCF=
(2x-3)
$ of the entire expression above results to
\begin{align*}
(2x-3)(x-12)
\end{align*}
