Critical points multivariable function

Find the cp of f(x,y)=6xy+x^2-y^3

First, find the first order partial derivatives.
f_x = 6y + 2x
f_y = 6x - 3y^2.

Set these equal to 0:
6y + 2x = 0 ==> x = -3y
6x - 3y^2 = 0 ==> 2x - y^2 = 0

Substituting the first equation into the second:
2(-3y) - y^2 = 0
==> -y(6 + y) = 0
==> y = 0, -6.

So, the critical points are (x, y) = (0, 0) and (18, -6).

I hope this helps!