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a^{2}\left(7a-6\right)-6\left(7a-6\right)
Do the grouping 7a^{3}-6a^{2}-42a+36=\left(7a^{3}-6a^{2}\right)+\left(-42a+36\right), and factor out a^{2} in the first and -6 in the second group.
\left(7a-6\right)\left(a^{2}-6\right)
Factor out common term 7a-6 by using distributive property. Polynomial a^{2}-6 is not factored since it does not have any rational roots.