Intermediate Algebra (6th Edition)

$2(2x-5)(3x+2)$
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}