Find all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying $$f\left(f(x)f(y)\right)+f(x+y)=f(xy)$$
The only thought i could get is clearly $f(x)=0$ satisfies. Also if $f(x)$ is an even function the functional equation is alsways true, but no clue for finding those functions.