Answer
$-3(2a+5b)(5a+2b)$
Work Step by Step
Factoring the negative $GCF=
-3
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-30a^2-87ab-30b^2
\\\\=
-3(10a^2+29ab+10b^2)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-3(10a^2+29ab+10b^2)
\end{array} has $ac=
10(10)=100
$ and $b=
29
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
25,4
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-3(10a^2+25ab+4ab+10b^2)
.\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}
-3[(10a^2+25ab)+(4ab+10b^2)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-3[5a(2a+5b)+2b(2a+5b)]
.\end{array}
Factoring the $GCF=
(3x-4y)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
-3[(2a+5b)(5a+2b)]
\\\\=
-3(2a+5b)(5a+2b)
.\end{array}