Is there a systematic way to solve equations in the braid groups? In particular, if B3 is the braid group on three strands with the presentation { a,b | aba = bab }, how do I find x so that xaxbx^-1b^-1x^-1 = bax^-1b^-1x (if such an x exists)?

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)?