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2x\left(x+c\right)-3b\left(x+c\right)
Do the grouping 2x^{2}+2xc-3bc-3bx=\left(2x^{2}+2xc\right)+\left(-3bc-3bx\right), and factor out 2x in the first and -3b in the second group.
\left(x+c\right)\left(2x-3b\right)
Factor out common term x+c by using distributive property.