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y\left(v-3\right)+6v\left(v-3\right)
Do the grouping vy-18v+6v^{2}-3y=\left(vy-3y\right)+\left(6v^{2}-18v\right), and factor out y in the first and 6v in the second group.
\left(v-3\right)\left(y+6v\right)
Factor out common term v-3 by using distributive property.