I'm looking for the name of this theorem:
Let $P$, $Q$ be languages. Let $X$ be a language variable. Then the language equation $X=PX + Q$ (here $+$ denotes union) has a solution $X=P^*Q$, and the solution is unique if the null string doesn't belong to $P$.
Arden's Rule.
(That was my answer, but the rules of Stackexchange force me to continue to at least 30 characters)