Problem

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

Tags: algebra, functional equation



Find all functions $f: \mathbb{R}\rightarrow \mathbb{R}$ such that for $\forall$ $x,y\in \mathbb{R}$ : $f(x+f(x+y))+xy=yf(x)+f(x)+f(y)+x$.