The Chain Rule & Implicit Differentiation · Superchallenge problem

Let $\varphi(p,q)$ be any smooth function of two variables, and suppose the equation $\varphi(x - 2z,\ y - 3z) = 0$ defines $z$ as a smooth function of $(x,y)$ near some point (with the needed partial derivative nonzero). Find the value of $2\dfrac{\partial z}{\partial x} + 3\dfrac{\partial z}{\partial y}$, which does not depend on $\varphi$ or on the point.