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10x^{2}+\left(-7y-14z\right)x-6y^{2}+27yz-12z^{2}
Consider 10x^{2}-7xy-6y^{2}-14xz+27yz-12z^{2} as a polynomial over variable x.
\left(2x+y-4z\right)\left(5x-6y+3z\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 10x^{2} and n divides the constant factor -6y^{2}+27yz-12z^{2}. One such factor is 2x+y-4z. Factor the polynomial by dividing it by this factor.