Answer
$2(2x-5)(3x+2)$
Work Step by Step
Factoring the $GCF=2$, then the given expression, $
12x^2-22x-20
$, is equivalent to
\begin{array}{l}
2(6x^2-11x-10)
.\end{array}
The two numbers whose product is $ac=
6(-10)=-60
$ and whose sum is $b=
-11
$ are $\{
-15,4
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
2(6x^2-11x-10)
$, is
\begin{array}{l}\require{cancel}
2(6x^2-15x+4x-10)
\\\\=
2[(6x^2-15x)+(4x-10)]
\\\\=
2[3x(2x-5)+2(2x-5)]
\\\\=
2[(2x-5)(3x+2)]
\\\\=
2(2x-5)(3x+2)
.\end{array}
