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9a\left(2a-3b\right)+7c\left(2a-3b\right)
Do the grouping 18a^{2}-27ab+14ac-21bc=\left(18a^{2}-27ab\right)+\left(14ac-21bc\right), and factor out 9a in the first and 7c in the second group.
\left(2a-3b\right)\left(9a+7c\right)
Factor out common term 2a-3b by using distributive property.