Answer
$3(2x+5y)(7x+4)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
42x^2+24x+105xy+60y
,$ factor first the $GCF.$. Then group the terms such that the factored form of the groupings will result to a factor that is common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=6,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
3(14x^2+8x+35xy+20y)
.\end{array}
Grouping the first and third terms and the second and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
3[(14x^2+35xy)+(8x+20y)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
3[7x(2x+5y)+4(2x+5y)]
.\end{array}
Factoring the $GCF=
(2x+5y)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
3[(2x+5y)(7x+4)]
\\\\=
3(2x+5y)(7x+4)
.\end{array}
