Let ω be the complex number cos⁡2π3+isin⁡2π3. Then the number of distinct complex numbers z satisfying z+1ωω2ωz+ω21ω21z+ω=0 is equal to _________.

ω=ei2π/3z+1ωω2ωz+ω21ω21z+ω=0z1ωω21z+ω2111z+ω=0 (Applying C1→C1+C2+C3 and using 1+ω+ω2=0 ) or   zz+ω2(z+ω)−1−ω(z+ω−1)+ω21−z−ω2=0or   z3=0or   z=0 is only solution.