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a\left(a-3\right)+2b\left(a-3\right)
Do the grouping a^{2}-3a+2ab-6b=\left(a^{2}-3a\right)+\left(2ab-6b\right), and factor out a in the first and 2b in the second group.
\left(a-3\right)\left(a+2b\right)
Factor out common term a-3 by using distributive property.