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3a^{2}\left(6a+5\right)-\left(6a+5\right)
Do the grouping 18a^{3}+15a^{2}-6a-5=\left(18a^{3}+15a^{2}\right)+\left(-6a-5\right), and factor out 3a^{2} in the first and -1 in the second group.
\left(6a+5\right)\left(3a^{2}-1\right)
Factor out common term 6a+5 by using distributive property. Polynomial 3a^{2}-1 is not factored since it does not have any rational roots.