Multivariable critical points I have the following function:
$\ f(x,y) = (x^3-y^2)(x-1) $
Expanding the brackets gives:
$\ f(x,y) = x^4 - x^3 - xy^2 + y^2 $
I understand to find the first derivative of both variables and set to zero:
$\ f_x ==> 4x^3 - 3x^2 - y^2 = 0.....[1] $ 
$\ f_y ==> y - 2xy = 0.....[2] $ 
$\ y = 2xy.....[3] $
Substituting [3] into [1]:
$\ 4x^3 - 3x^2 - 4x^2y^2 = 0 $ 
$\ x^2(4x - 3 - y^2) = 0$
I am stuck at this point and can not factorise further to find the critical points. Any hints or clues would be helpful. Thank you. 

The second partial derivative is $-2xy+2y$ which gives $-xy+y=y(-x+1)=0$, $y=0$ or $x=1$. By replacing $y=0$ you have  $4x^3-3x^2=0$  or $x=1$,  $4-3-y^2=0$.
