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6\left(7abc^{2}-2a^{2}bc+5ab^{2}c\right)
Factor out 6.
abc\left(7c-2a+5b\right)
Consider 7abc^{2}-2a^{2}bc+5ab^{2}c. Factor out abc.
6abc\left(-2a+5b+7c\right)
Rewrite the complete factored expression.