  The known facts about solvability of equations over groups are considered
from a more general point of view. A generalized version of the theorem about
solvability of unimodular equations over torsion-free groups is proved. In a
special case, this generalized version become a multivariable variant of this
theorem. For unimodular equations over torsion free groups, we prove an
analogue of Magnus's Freiheitssatz, which asserts that there exists a solution
with good behavior with respect to free factors of the initial group.
