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2x^{4}\left(-2x+3\right)-3\left(-2x+3\right)
Do the grouping -4x^{5}+6x^{4}+6x-9=\left(-4x^{5}+6x^{4}\right)+\left(6x-9\right), and factor out 2x^{4} in the first and -3 in the second group.
\left(-2x+3\right)\left(2x^{4}-3\right)
Factor out common term -2x+3 by using distributive property. Polynomial 2x^{4}-3 is not factored since it does not have any rational roots.