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2a^{2}\left(3a-7\right)+5x\left(3a-7\right)
Do the grouping 6a^{3}-14a^{2}+15ax-35x=\left(6a^{3}-14a^{2}\right)+\left(15ax-35x\right), and factor out 2a^{2} in the first and 5x in the second group.
\left(3a-7\right)\left(2a^{2}+5x\right)
Factor out common term 3a-7 by using distributive property.