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6m^{2}+\left(-13n-9\right)m+6n^{2}+6n
Consider 6m^{2}-13mn+6n^{2}-9m+6n as a polynomial over variable m.
\left(3m-2n\right)\left(2m-3n-3\right)
Find one factor of the form km^{p}+q, where km^{p} divides the monomial with the highest power 6m^{2} and q divides the constant factor 6n^{2}+6n. One such factor is 3m-2n. Factor the polynomial by dividing it by this factor.