Find all function $f: \Bbb{N}_0 \rightarrow \Bbb{N}_0 $ satisfying the equation $f(f(n) + f(n) = 2n +3k$ for all $n \in \Bbb{N}_0 $ where $k$ is a fixed natural number.
I have proceeded with solution to a point but I am not able to go further
so lets say $f(0)=m$ $\implies$
$f(m) =3k-m$
$f(3k-m)=f(f(m)=2m+3k-f(m)=3m$
$f(3m)=f(f(3k-m))=2(3k-m)+3k-f(3k-m)=9k-5m $
after this I am not able to proceed through