Answer
$(2t+5)(4t-3)$
Work Step by Step
The given expression, $
14t+8t^2-15
,$ can be re-written as
\begin{array}{l}
8t^2+14t-15
.\end{array}
The two numbers whose product is $ac=
8(-15)=-120
$ and whose sum is $b=
14
$ are $\{
20,-6
\}$. Using these two numbers to decompose the middle term of the expression, $
8t^2+14t-15
,$ then the factored form is
\begin{array}{l}
8t^2+20t-6t-15
\\\\=
(8t^2+20t)-(6t+15)
\\\\=
4t(2t+5)-3(2t+5)
\\\\=
(2t+5)(4t-3)
.\end{array}
