Answer
$(3a-5b)(4a-3b)$
Work Step by Step
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}