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5y\left(y-3\right)+u\left(y-3\right)
Do the grouping yu-15y-3u+5y^{2}=\left(5y^{2}-15y\right)+\left(yu-3u\right), and factor out 5y in the first and u in the second group.
\left(y-3\right)\left(5y+u\right)
Factor out common term y-3 by using distributive property.