The given equation is: $(x-1)^{3}=-8$
or, $((x-1)/-2)^{3}=1$
Let $((x-1)/-2)= Z$
So, the equation will be changed to: $Z^{3}=1$
The roots will be $Z=1, ω, ω^{2}$
Putting back the value of $Z$
$\quad (x-1)/-2 = 1, ω, ω^{2}$
$\quad \implies x= -1, 1-2$ω$, 1-2ω^{2}$