I need help with this equation with complex numbers

Question

I have to solve $z^3(z-i)-1-2z^2-z^4=0$.
I got $z^4-iz^3-1-2z^2-z^4=0$ and then $-iz^3-1-2z^2=0$ but now I don't know how to continue to find the three solutions.

Could anyone give me a suggestion? Thanks.

Answer 1

Hint: $z=i$ is one root. Factor out $(z-i)$ to find the other two roots.