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6\left(4a^{3}b^{2}c-3a^{2}b^{2}c^{2}+5a^{2}bc\right)
Factor out 6.
a^{2}bc\left(4ab-3bc+5\right)
Consider 4a^{3}b^{2}c-3a^{2}b^{2}c^{2}+5a^{2}bc. Factor out a^{2}bc.
6a^{2}bc\left(4ab-3bc+5\right)
Rewrite the complete factored expression.