I think completing the square might be better in this case...
From here, you should convert to polars to find the four values of .
It's very clear that z = -1 is a solution to . Therefore z + 1 is a factor. Divide z + 1 into to get a cubic factor. It is very clear that z + 1 is also a factor of the cubic. Divide it into the cubic to get a quadratic factor. Factorise the quadratic in the usual way.
From the factor you get the solutions. There is sure to be examples like this in your class notes and textbook. Go back and review this material.