#### Answer

$-2t(t+2)(t+3)$

#### Work Step by Step

Factoring the negative $GCF=
-2t
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-2t^3-10t^2-12t
\\\\=
-2t(t^2+5t+6)
.\end{array}
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-2t(t^2+5t+6)
\end{array} has $c=
6
$ and $b=
5
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
2,3
\right\}.$ Using these two numbers, the $\text{
expression
}$ above is equivalent to
\begin{array}{l}\require{cancel}
-2t(t+2)(t+3)
.\end{array}