I need to find the vertical tangents for this function

$\displaystyle 2y^3+y^3-y^5=x^4-2x^3+x^2$

I got this for the derivative

$\displaystyle dy/dx=(4X^3-6x^2+2x)/(6y^2+2y-5y^4)$

I know to set the denominator equal to zero and from there I'm stuck

Thanks in advance!