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