  In this paper, we consider some generalized commutator equations in a finite
group and show that the number of solutions of such equations are characters of
that group. We also obtain explicit formula for this character, considering the
equation $[\cdots[[[x_1,x_2],x_3],$ $x_4],\cdots, x_n] = g$, for some
well-known classes of finite groups in terms of orders of the group, its center
and its commutator subgroup. This paper is an extension of the works of
Pournaki and Sobhani in [22].
