Well it's a sixth order polynomial. How many solutions do you expect from the fundamental theorem of algebra.

Then you're trying to solve $\displaystyle \begin{align*} z^6 - z^5 + 2z^4 - 5z^3 + 3z^2 = 0 \end{align*}$, what methods do you know to solve polynomials? Can you at least pull out a factor?