Answer
$(2y+3)(6y-5)$
Work Step by Step
The given expression, $
8y-15+12y^2
,$ can be re-written as
\begin{array}{l}
12y^2+8y-15
.\end{array}
The two numbers whose product is $ac=
12(-15)=-180
$ and whose sum is $b=
8
$ are $\{
18,-10
\}$. Using these two numbers to decompose the middle term of the expression, $
8t^2+14t-15
,$ then the factored form is
\begin{array}{l}
12y^2+18y-10y-15
\\\\=
(12y^2+18y)-(10y+15)
\\\\=
6y(2y+3)-5(2y+3)
\\\\=
(2y+3)(6y-5)
.\end{array}
