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6m\left(7c+6d\right)-n^{2}\left(7c+6d\right)
Do the grouping 42mc+36md-7n^{2}c-6n^{2}d=\left(42mc+36md\right)+\left(-7n^{2}c-6n^{2}d\right), and factor out 6m in the first and -n^{2} in the second group.
\left(7c+6d\right)\left(6m-n^{2}\right)
Factor out common term 7c+6d by using distributive property.