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3\left(-mx-3ny+3nz+3nx+my-mz\right)
Factor out 3.
m\left(-x+y-z\right)-3n\left(-x+y-z\right)
Consider -mx-3ny+3nz+3nx+my-mz. Do the grouping -mx-3ny+3nz+3nx+my-mz=\left(-mx+my-mz\right)+\left(3nx-3ny+3nz\right), and factor out m in the first and -3n in the second group.
\left(-x+y-z\right)\left(m-3n\right)
Factor out common term -x+y-z by using distributive property.
3\left(m-3n\right)\left(-x+y-z\right)
Rewrite the complete factored expression.