Answer
$(x-3)(x+12)$
Work Step by Step
Let $z=
(x+3)
.$ The given expression, $
(x+3)^2+3(x+3)-54
,$ is equivalent to
\begin{align*}
z^2+3z-54
.\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c=
-54
$ and $b=
3
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-6,9
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{align*}
(z-6)(z+9)
.\end{align*}
Substituting back $z=(x+3),$ the expression above is equivalent to
\begin{align*}
&
(x+3-6)(x+3+9)
\\&=
(x-3)(x+12)
.\end{align*}
