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6x^{2}\left(7x-4\right)-5\left(7x-4\right)
Do the grouping 42x^{3}-24x^{2}-35x+20=\left(42x^{3}-24x^{2}\right)+\left(-35x+20\right), and factor out 6x^{2} in the first and -5 in the second group.
\left(7x-4\right)\left(6x^{2}-5\right)
Factor out common term 7x-4 by using distributive property. Polynomial 6x^{2}-5 is not factored since it does not have any rational roots.