This is a question from my calculus 3 class.

"Find all points on the surface at which the tangent plane is horizontal."

z = x^2 - xy + y^2 - 2x + 4y

Okay, so I'm not sure where to begin. I know that the partial derivatives z_x and z_y are both zero. And so I've thought of making a tangent equation but I got stuck.

Tangent plane = (z - z0) ?

I'm not sure if I have to solve for x and y in the given equation, or really what I have to do in general.

Can anyone give me a push in the right direction? Maybe I'm over-thinking this problem.