  The Levin conjecture was proposed by Levin in 1962 which conjectures the
solvability of any group equation with coefficients in a torsion free group.
The Levin conjecture is recently shown to hold for group equations of length
seven by weight test and curvature distribution. These methods are applied on a
group equation of length nine to explore the validity of Levin conjecture. It
is found that the Levin conjecture has an affirmative answer for this equation
modulo some exceptional cases.
