Need help finding the Horizontal Tangent of an Implicit Equation

Question

I am given the equation: $(x^3) + (y^3) - (72xy) = 0 $. I found the derivative to be: $(-3x^2 + 72y)/(3y^2 - 72 x) $ I know that the numerator of the derivative must be set to $0$ in order to proceed but I am unsure of what to do after that.
Any help would be greatly appreciated

Answer 1

with $$y=y(x)$$ we get $$3x^2+3y^2y'-72y-72xy'=0$$ from here we get $$y'(3y^2-72x)=72y-3x^2$$