Answer
$(3x-4)(x+5)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression
\begin{align*}
3x^2+11x-20
\end{align*} has $ac=
3(-20)=-60
$ and $b=
11
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-4,15
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
3x^2-4x+15x-20
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(3x^2-4x)+(15x-20)
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
x(3x-4)+5(3x-4)
.\end{align*}
Factoring the $GCF=
(3x-4)
$ of the entire expression above results to
\begin{align*}
(3x-4)(x+5)
.\end{align*}
