We discuss the following question of G. Makanin from "Kourovka notebook": does there exist an algorithm to determine is for an arbitrary pair of words U and V of a free group Fn and an arbitrary automorphism φ ∈ Aut(Fn) the equation φ(X)U = VX solvable in Fn? We give the affirmative answer in the case when an automorphism is virtually inner, i.e. some its non-zero power is an inner automorphism of Fn.