Why are you restricting the solution to only one moment equation?
Maybe because there is a famous theorem that says when
all the forces are in balance, the torque around one pivot
is equal to the torque around any other pivot.
So writing additional moment equations is guaranteed to not
tell you anything you didn't already know.
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More generally, the torque around one pivot differs from
the torque around any other pivot by an amount given by
(how much you moved the pivot) /\ (net unbalanced force)