How to solve $(x-2)f(y)+f(y+2f(x)) = f(x + yf(x))$?

Question

I'm trying to solve this task:

Find all functions $f:\mathbb{R} \to \mathbb{R}$ that satisfy: $(x-2)f(y)+f(y+2f(x)) = f(x + yf(x))$

I plugged in $x=2$:

$f(y + 2f(2)) = f(2 + yf(2))$

If I assume that values are equal:

$y + 2f(2) = 2 + yf(2)$

Then I get:

$f(2) = 1$

So then I randomly checked $f(x) = x - 1$ and it turned out to be a solution.

I then tried some other things but didn't really get anything.

Could somebody please give a hint as to how to find other solutions?

Thanks in advance.

EDIT: found this question