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3r^{2}\left(4r+5\right)-4\left(4r+5\right)
Do the grouping 12r^{3}+15r^{2}-16r-20=\left(12r^{3}+15r^{2}\right)+\left(-16r-20\right), and factor out 3r^{2} in the first and -4 in the second group.
\left(4r+5\right)\left(3r^{2}-4\right)
Factor out common term 4r+5 by using distributive property. Polynomial 3r^{2}-4 is not factored since it does not have any rational roots.