Answer
$(2x+9)(7x+5)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
14x^2+73x+45
\end{array} has $ac=
14(45)=630
$ and $b=
73
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
63,10
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
14x^2+63x+10x+45
.\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}
(14x^2+63x)+(10x+45)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
7x(2x+9)+5(2x+9)
.\end{array}
Factoring the $GCF=
(2x+9)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2x+9)(7x+5)
.\end{array}
