functional equations - Finding all real valued functions that satisfy $f(f(y) + xf(x)) = y + (f(x))^2$

I would like some help with finding all real valued functions that satisfy this equation:

$f(f(y) + xf(x)) = y + (f(x))^2$

I tried the usual substitutions like $x = y = 0$, but my experience with this kind of problem is very limited.

EDIT: I'm an idiot and copied the wrong right side. Updated it now.

Answer

$$f(f(y) + xf(x)) = y + f^2(x)$$
Let $x=0$, then :
$$f(f(y))=y+f^2(0)$$

So as $y$ is one-one and onto and invertible, that said that $f$ is onto, so there's no harm supposing that $f(x)=0$ or $x=f^{-1}(0)$:
$$f(f(y))=y\implies f(y)=f^{-1}y$$
Does that give you a hint[$f$ is a one-one onto invertible self-inverse function]. Try $f(x)=x$ or $f(x)=-x$.