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x\left(-v+6\right)+2v\left(-v+6\right)
Do the grouping 12v-vx-2v^{2}+6x=\left(-vx+6x\right)+\left(-2v^{2}+12v\right), and factor out x in the first and 2v in the second group.
\left(-v+6\right)\left(x+2v\right)
Factor out common term -v+6 by using distributive property.