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