Solve for $Q$: $ Q = (1-p) + p \cdot Q^{z-1} $

Question

Solve for $Q$: $Q = (1-p) + p \cdot Q^{z-1} $, where $p\ \displaystyle\epsilon[0,1]$ and $z$ is positive integer.

My try:

$Q-1=p(Q^{z-1}-1)\implies Q-1=p(Q-1)(Q^{z-2}+Q^{z-3}+....+1)$ $\implies Q=1$ is one solution, how to get others, please help.