Boundary value problems for equations of variable type are one of the classical objects of research. The work investigates the solvability of boundary value problems for equations of variable type. Equations of variable type have special practical significance. In addition, their research is related to the development of various branches of mathematics, in particular, the theory of partial differential equations and the theory of functional analysis. The purpose of this work consists in studying the solvability of a boundary value problem for an equation of variable type. The solvability of an equation of variable type is proven using the regularization method, Hölder and Young inequalities and a priori estimation methods. At the same time, this work proves the regularity of the solution and the uniqueness of the boundary value problem even for the case when the  term is on the left side of the equation. Boundary value problems for equations of variable type are used in many fields of science, in the field of physics, quantum electronics, plasma physics, nuclear physics, and the Keldysh equation, which is an example of an equation of variable type, closely Tricomi problem associated with aircraft design calculations has contributed to field of gas dynamics. In addition, it is used in the fields of mechanics, geophysics, chemistry, molecular biology and natural sciences.