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x\left(b+3c\right)-2r\left(b+3c\right)
Do the grouping bx+3cx-2br-6cr=\left(bx+3cx\right)+\left(-2br-6cr\right), and factor out x in the first and -2r in the second group.
\left(b+3c\right)\left(x-2r\right)
Factor out common term b+3c by using distributive property.