Factor 6xy^2(3y-x)-3x^2(x-3y)^2

Question

I am close but can't seem to figure out how to factor 6xy^2(3y-x)-3x^2(x-3y)^2

Please help me.  I have the answer but need to see the steps.  The answer is -3x(x-3y)(x-y)(x-2y).  I got the first half of the answer but can't figure out the last 2 parenthesis.  Going nutz!

Emilia.

Answer 1

6xy²(3y-x)-3x²(x-3y)²=

-6xy²(x-3y)-3x²(x-3y)²=

-3x(2y²+x(x-3y))(x-3y)=

-3x(x²-3xy+2y²)(x-3y)=

-3x(x-y)(x-2y)(x-3y).