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4z\left(z+3\right)-a\left(z+3\right)
Do the grouping 4z^{2}+12z-az-3a=\left(4z^{2}+12z\right)+\left(-az-3a\right), and factor out 4z in the first and -a in the second group.
\left(z+3\right)\left(4z-a\right)
Factor out common term z+3 by using distributive property.