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a^{2}\left(5z-4c\right)+3x\left(5z-4c\right)
Do the grouping 5a^{2}z-4a^{2}c+15xz-12xc=\left(5a^{2}z-4a^{2}c\right)+\left(15xz-12xc\right), and factor out a^{2} in the first and 3x in the second group.
\left(5z-4c\right)\left(a^{2}+3x\right)
Factor out common term 5z-4c by using distributive property.