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y\left(-4x^{2}+12xy-9y^{2}\right)
Factor out y.
-4x^{2}+12yx-9y^{2}
Consider -4x^{2}+12xy-9y^{2}. Consider -4x^{2}+12xy-9y^{2} as a polynomial over variable x.
\left(2x-3y\right)\left(-2x+3y\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 -9y^{2}. One such factor is 2x-3y. Factor the polynomial by dividing it by this factor.
y\left(2x-3y\right)\left(-2x+3y\right)
Rewrite the complete factored expression.