cal3/algebra help me!

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Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= -3yx^2-3xy^2+36xy
I really need help answering this one!! Please answer in detail! Thank you
This is what I have so far...
D=FxxFyy-(Fxy)^2=(-6y)(-6x)-(-6x-6y+36)^2
= 36xy-36(x+y-6)^2
Now set D=0 but I don't know how to solve it?? 36xy-36(x+y-6^2=0
Set Fx=0=-6x-6y+36 and set Fy=0=-6xy-3y^2+36y
I need help with the algebra, its been so long

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