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2x\left(5x+y\right)-3\left(5x+y\right)
Do the grouping 10x^{2}+2xy-15x-3y=\left(10x^{2}+2xy\right)+\left(-15x-3y\right), and factor out 2x in the first and -3 in the second group.
\left(5x+y\right)\left(2x-3\right)
Factor out common term 5x+y by using distributive property.