geometry - Question about solved problem

I am struggling to understand a step in the accepted solution of
How Can One Prove $\cos(\pi/7) + \cos(3 \pi/7) + \cos(5 \pi/7) = 1/2$.

I have been new to this site, I can not figure out where to ask this question.

Can someone please enlighten me why $u^5+u^3+u=a$ is equivalent to $ua+1=a$?

With algebra, I just get stuck. I also can't find any property that establishes the equivalence.

Thanks in advance.