Given the equation $$\left| x\; -\; c \right|\; +\; \left| x\; +\; c \right|\; -\; \left| y \right|\; -\; \left| \left| x\; -\; c \right|\; -\; \left| y \right| \right|\; = b \text{,} -c, c, b \in \mathbb{R}\text{,}$$ what are it's turning points and how many solutions to that equation is?
A little edit: By turning points I mean a points, at which absolute values change it's sign.
Obviously, those are $-c, c$ for $x$ and $0$ for $y$, but I am not sure.