Is there a systematic way to solve equations in the braid groups? In particular, if $B_3$ is the braid group on three strands with the presentation $\{ a,b\ | \ aba = bab \}$, how do I find $x$ so that $xaxbx^{-1}b^{-1}x^{-1} = bax^{-1}b^{-1}x$ (if such an $x$ exists)?