For what value of $a$ does the equation $|x(x-4)|=a$ have exactly 3 real solutions? I simplified the equation and got two cases where $$x(x-4)=a$$
and 
$$x(x-4)=-a.$$
How do I go after that. I know how you could get $2$ solutions or $4$ solutions, but how do you get $3$ solutions?

Hint:
Linear equations have one solution
Quadratic equations have two solutions 
Hence cubic equations will have 3 solutions
