How do i find the singular points of the following curve in A^2(C) OR prove that there are no singular points? (where A is affine space and C is complex numbers)

The curve is

(x^2)(y^2)-6(x^2)+2xy-6(y^2)+25=0

Taking partial derivatives i get the jacobian matrix

J = (2x(y^2)-12x+2y 2(x^2)y+2x-12y)

I do not know how to proceed from here.

Any help is appreciated.

Thanks