Answer
$(3t+7)(2t+1)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
6t^2+17t+7
\end{array} has $ac=
6(7)=42
$ and $b=
17
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
14,3
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
6t^2+14t+3t+7
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(6t^2+14t)+(3t+7)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2t(3t+7)+(3t+7)
.\end{array}
Factoring the $GCF=
(3t+7)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(3t+7)(2t+1)
.\end{array}
