Quote by Miriverite
If a=b adn b=d, then my above function satisfies for all a  that's good enough, yes?

It does, but its not the most general solution...which is what you are looking for.
(3a+c) = (3d+b) = 0 does
not mean that a=b and b=d....the
only requirement is that c=3a and b=3d.