Answer
$(5a-3)(3a-1)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
15a^2-14a+3
\end{array} has $ac=
15(3)=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}
15a^2-9a-5a+3
.\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}
(15a^2-9a)-(5a-3)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
3a(5a-3)-(5a-3)
.\end{array}
Factoring the $GCF=
(5a-3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(5a-3)(3a-1)
.\end{array}