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7x^{2}\left(x+2\right)-6\left(x+2\right)
Do the grouping 7x^{3}-12-6x+14x^{2}=\left(7x^{3}+14x^{2}\right)+\left(-6x-12\right), and factor out 7x^{2} in the first and -6 in the second group.
\left(x+2\right)\left(7x^{2}-6\right)
Factor out common term x+2 by using distributive property. Polynomial 7x^{2}-6 is not factored since it does not have any rational roots.