Intermediate Algebra (6th Edition)

$(3a-5b)(4a-3b)$
The two numbers whose product is $ac= 12(15)=180$ and whose sum is $b= -29$ are $\{ -20,-9 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $12a^2-29ab+15b^2$, is \begin{array}{l}\require{cancel} 12a^2-20ab-9ab+15b^2 \\\\= (12a^2-20ab)-(9ab-15b^2) \\\\= 4a(3a-5b)-3b(3a-5b) \\\\= (3a-5b)(4a-3b) .\end{array}