You need to multiply both sides by `z - 1` such that:
`(z-1)(z^4+z^3+z^2+z+1) = 0*(z-1)`
You need to convert the product to the left side into a difference of powers such that:
`z^5 - 1 = 0 => z^5 = 1 => z^5 = root(5)1 => z = 1`
Since the graph below representing the function `f(x)=x^4+x^3+x^2+x+1` , does not intercept x axis, hence, the equation has no real roots but 4 complex roots.
Thank you, sciencesolve! :*