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3\left(a^{2}+3a+2ac+6c\right)
Factor out 3.
a\left(a+3\right)+2c\left(a+3\right)
Consider a^{2}+3a+2ac+6c. Do the grouping a^{2}+3a+2ac+6c=\left(a^{2}+3a\right)+\left(2ac+6c\right), and factor out a in the first and 2c in the second group.
\left(a+3\right)\left(a+2c\right)
Factor out common term a+3 by using distributive property.
3\left(a+3\right)\left(a+2c\right)
Rewrite the complete factored expression.