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2m\left(n+3\right)+n\left(n+3\right)
Do the grouping 6m+2mn+3n+n^{2}=\left(6m+2mn\right)+\left(3n+n^{2}\right), and factor out 2m in the first and n in the second group.
\left(n+3\right)\left(2m+n\right)
Factor out common term n+3 by using distributive property.