Answer
$-2(x-24)(x+3)$
Work Step by Step
Factoring the negative $GCF=
-2
$, the given expression, $
-2x^2+42x+144
,$ is equivalent to
\begin{array}{l}
-2(x^2-21x-72)
.\end{array}
The 2 numbers whose product is $ac=
1(-72)=-72
$ and whose sum is $b=
-21
$ are $\left\{
-24,3
\right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then
\begin{array}{l}
-2(x^2-24x+3x-72)
\\\\=
-2[(x^2-24x)+(3x-72)]
\\\\=
-2[x(x-24)+3(x-24)]
\\\\=
-2[(x-24)(x+3)]
\\\\=
-2(x-24)(x+3)
.\end{array}