Answer
$(t+1)(9t+5)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
9t^2+14t+5
\end{array} has $ac=
9(5)=45
$ and $b=
14
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
9,5
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
9t^2+9t+5t+5
.\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}
(9t^2+9t)+(5t+5)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
9t(t+1)+5(t+1)
.\end{array}
Factoring the $GCF=
(t+1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(t+1)(9t+5)
.\end{array}