How to solve a complex polynomial? 
*

*Solve:
$$ z^3 - 3z^2 + 6z - 4 = 0$$


How do I solve this?
Can I do it by basically letting $ z = x + iy$ such that $ i = \sqrt{-1}$ and $ x, y \in \mathbf R $ and then substitute that into the equation and get a crazy long equation? If I did that I suspect I wouldn't be able to decipher the imaginary part of the equation.
Or should I change it to one of the forms below:
$$ z^n = r^n \mathbf{cis} n \theta $$
$$ z^n = r^n e^{n\theta i} $$
And then plug that into the equation? I did that. But it looked unsolvable. I'm so confused.

@Petch Puttichai , after we've guessed the root say $p(1)$, how do we find the other factors , is it that we divide the polynomial with first factor , are there any other methods ? 
For example if I have a polynomial of $z^4+z^3+... $ after we find the first root by guessing, how to get the other polynomial which I think should be of the form $z^3+z^2+...$.
Thanks for all your help.
Arif
