tangent plane of implicit function

question: surface Q:$\displaystyle 6x^2+3y^2+3z^2-6yz-2y-2z=0$ has exactly one horizontal tangent plane. Find it's equation and the point of tangency. Hint: there is no point on the surface below this plane

work: I took the partial derivatives and set them = 0. So I get x=0, and I used this to deduce that z=y (is this right?).

problem: the equation of a tangent plane requires me to compute f(a,b) but I can't do this since Q is an implicit function.

I haven't learned about vectors yet