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u^{2}\left(5u-6\right)+6\left(5u-6\right)
Do the grouping 5u^{3}-6u^{2}+30u-36=\left(5u^{3}-6u^{2}\right)+\left(30u-36\right), and factor out u^{2} in the first and 6 in the second group.
\left(5u-6\right)\left(u^{2}+6\right)
Factor out common term 5u-6 by using distributive property. Polynomial u^{2}+6 is not factored since it does not have any rational roots.