Solving equation with many exponents for same variable

Question

$1.32=5(r + r^4) + 10 (r^2 + r^3) + r^5 + 1$

How would one solve an equation like this?

Any help would be appreciated thanks.

Answer 1

Since the RHS equals $(r+1)^5$, one has $$1.32=(r+1)^5\Rightarrow r+1=1.32^{\frac 15}\Rightarrow r=1.32^{\frac 15}-1.$$