The paper describes the general form of functional-differential equations of the first order with $m (m\ge 1)$ delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation \[ f(t, uv, u_{1}v_{1}, \ldots , u_{m}v_{m}) = f(x, v, v_{1}, \ldots , v_{m})g(t, x, u, u_{1}, \ldots , u_{m})u + h(t, x, u, u_{1}, \ldots , u_{m})v \] for $u\ne 0$ is solved on $\mathbb R$ and a method of proof by J. Aczél is applied.