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