Let G be a non-trivial torsion free group and t be an unknown. In this
paper we consider three equations (over G) of arbitrary length and show that
they have a solution (over G) provided two relations among their coefficients
hold. Such equations appear for all lengths greater than or equal to eight and
the results presented in this article can substantially simplify their
solution.Comment: arXiv admin note: substantial text overlap with arXiv:1903.0650