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4x^{2}+\left(-4y-12\right)x-3y^{2}-6y
Consider 4x^{2}-4xy-3y^{2}-12x-6y as a polynomial over variable x.
\left(2x+y\right)\left(2x-3y-6\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 4x^{2} and n divides the constant factor -3y^{2}-6y. One such factor is 2x+y. Factor the polynomial by dividing it by this factor.