This paper presents a PSPACE algorithm which yields a finite graph of exponential size that describes the set of all solutions of equations in free groups as well as the set of all solutions of equations with rational constraints in free monoids. This became possible due to the recent recompression technique.While this technique was successfully applied for pure word equations without involution or rational constraints it could not be used as a black box for free groups. Actually, the presence of an involution and rational constraints complicates the situation and some additional analysis is necessary. Still, the technique is general enough to accommodate both extensions. In the end, it simplifies proofs that satisfiability of word equations is in PSPACE and the corresponding result for equations in free groups with rational constraints. As a byproduct we can decide in PSPACE whether the solution set is finite.