If a≠b≠c,  one value of x which satisfies the equation 0x−ax−bx+a0x−cx+bx+c0=0  is given by

By putting x=0  to    0x−ax−bx+a0x−cx+bx+c0   Then we get 0−a−ba0−cbc0 This is skew-symmetric determinant.This determinant is a skew-symmetric determinant of order 3 (as odd number) which is definitely 0.So, x=0  satisfies the given equation.