Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 57

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

The two numbers whose product is $ac= 10(-6)=-60 $ and whose sum is $b= -11 $ are $\{ -15,4 \}$. Using these two numbers to decompose the middle term of the expression, $ 10x^2-11x-6 ,$ then the factored form is \begin{array}{l} 10x^2-15x+4x-6 \\\\= 5x(2x-3)+2(2x-3) \\\\= (2x-3)(5x+2) .\end{array}