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2n^{2}\left(2n-3\right)+2n-3
Do the grouping 4n^{3}-6n^{2}+2n-3=\left(4n^{3}-6n^{2}\right)+\left(2n-3\right), and factor out 2n^{2} in 4n^{3}-6n^{2}.
\left(2n-3\right)\left(2n^{2}+1\right)
Factor out common term 2n-3 by using distributive property. Polynomial 2n^{2}+1 is not factored since it does not have any rational roots.