How do I solve the following equation: $z^4+z^3+z+1=0$ Is there an existing method to solve the following equation:
$z^4+z^3+z+1=0$?

Hint: 
$$z^4 + z^3 + z + 1 = z^4 + z + z^3 + 1 = z(z^3+1) + z^3 + 1 = (z+1)(z^3 + 1)$$
