Answer
$(2t+5)(2t+1)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
4t^2+12t+5
\end{array} has $ac=
4(5)=20
$ and $b=
12
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
10,2
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
4t^2+10t+2t+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}
(4t^2+10t)+(2t+5)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2t(2t+5)+(2t+5)
.\end{array}
Factoring the $GCF=
(2t+5)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2t+5)(2t+1)
.\end{array}