RU-ALLRUSSIAN 1974 Problem 6

Find all real a, b, c such that $\mathrm{la x} + \mathrm{by} + \mathrm{czl} + \mathrm{lbx} + \mathrm{cy} + \mathrm{azl} + \mathrm{lcx} + \mathrm{ay} + \mathrm{bzl} = \mathrm{lx} + \mathrm{y} + \mathrm{zl}$ for all real x, y, z.