Answer
$2n(m-5)(m^2-3)$
Work Step by Step
Factoring the $GCF=
2n
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
2m^3n-10m^2n-6mn+30n
\\\\=
2n(m^3-5m^2-3m+15)
.\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}
2n(m^3-5m^2-3m+15)
\\\\=
2n[(m^3-5m^2)-(3m-15)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2n[m^2(m-5)-3(m-5)]
.\end{array}
Factoring the $GCF=
(m-5)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
2n[(m-5)(m^2-3)]
\\\\=
2n(m-5)(m^2-3)
.\end{array}
