Answer
$(x+12)(x-6)$
Work Step by Step
In decreasing order of exponents, the given expression, $
x^2-72+6x
,$ is equivalent to
\begin{array}{l}
x^2+6x-72
.\end{array}
The 2 numbers whose product is $ac=
1(-72)=-72
$ and whose sum is $b=
6
$ are $\left\{
12,-6
\right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then
\begin{array}{l}
x^2+12x-6x-72
\\\\=
(x^2+12x)-(6x+72)
\\\\=
x(x+12)-6(x+12)
\\\\=
(x+12)(x-6)
.\end{array}
