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x^{2}+\left(y+5\right)x-6y^{2}+35y-36
Consider x^{2}+xy-6y^{2}+5x+35y-36 as a polynomial over variable x.
\left(x+3y-4\right)\left(x-2y+9\right)
Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor -6y^{2}+35y-36. One such factor is x+3y-4. Factor the polynomial by dividing it by this factor.