Find roots of unity

Question

Find the roots of $6z^5 + 15z^4 + 20z^3 + 15z^2 + 6z + 1 = 0.$

I know how to do this without the coefficients, but I do not know what to do in this problem.

Thanks

Answer 1

Hint: We are solving $(z+1)^6-z^6=0$, or equivalently $\left(1+\frac{1}{z}\right)^6=1$.