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2x\left(3x-2y\right)+3x-2y
Do the grouping 6x^{2}-4xy+3x-2y=\left(6x^{2}-4xy\right)+\left(3x-2y\right), and factor out 2x in 6x^{2}-4xy.
\left(3x-2y\right)\left(2x+1\right)
Factor out common term 3x-2y by using distributive property.