Prove that the function is injective

Question

Prove that this function is injective. $$f(x + 2xf(y)^2) = yf(x) + f(f(y) + 1)$$

I try to fix $x$ and put two values for $y$: $a$ and $b$, but I can't prove it.

Maybe it is better to fix $y$ and choose two values for $x$?