Solution to real and complex polynomial function?

[Mandynash]

Homework Statement

Hi, I have been given the polynomial function P(z)=4z^4 -12z^2 +3z +19
I need to Establish the main technique/s required to solve the polynomial.
Then I need to find the solution of the polynomial?

Any help would be greatly appreciated because I have no idea where to start.

Homework Equations

P(z)=4z^4 -12z^2 +3z +19

The Attempt at a Solution

 

[lanedance]

by solve i guess you mean factor, well you can tell it has no real roots, how about using the fact its roots must be congjugates then