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