(2z+2)(z^5-3)+6=0 simplify the left side
2z^6 + 2z^5 - 6z - 6 + 6 = 0
2z^6 + 2z^5 - 6z = 0 divide through by 2
z^6 + z^5 - 3z = 0 factor
z(z^5 + z^4 - 3) = 0 z = 0 is one solution
To find the other...we need to solve this
z^5 + z^4 - 3 = 0 this would be a little difficult by hand.......WolframAlpha gives one "real" solution of : z ≈ 1.09404