# Solve recursive equation in lambda calculus

I need to find such F, so that for any M $FM = MF$. I can't figure out, how to bring this equation to the form like this: $F = TF$, so that I could just apply Y combinator

$F = \lambda x.xF$
Instead of using $Y$, we can use $R=\lambda x.xx$ for recursion.
$F = R(\lambda fM.M(Rf))$
$$FM = R(\lambda fM.M(Rf)) \\ = (\lambda x.xx)(\lambda fM.M(Rf))M \\ = (\lambda fM.M(Rf))(\lambda fM.M(Rf))M \\ = M(R(\lambda fM.M(Rf))) \\ = MF$$