(z-2/6z+(z-2) ^2)+(z+4) ^2-12/z^3-2^3) — (1/z-2): z^3+2z^2+2z+4/z^3-2z^2+2z-4

2z^4 — 3z^3+4z^2 — 3z+2=0 => Dividing by z^2, 2z^2 — 3z+4 — 3/z+2/z^2=0 => 2 (z^2+1/z^2) — 3 (z+1/z)+4=0 => 2 [ (z+1/z) ^2 — 2] — 3 (z+1/z)+4=0 => 2 (z+1/z) ^2 — 3 (z+1/z)=0 => (z+1/z) [2 (z+1/z) — 3]=0 => (z^2+1) (2z^2 — 3z+2)=0 => (z^2+1) (2z^2 — 3z+2)=0 => z^2+1=0 or 2z^2 — 3z+2=0 => z=± i or z=(1/2) [3 ± √ (9 — 16) ] => z=± i or z=(3/2) ± i (7/2)