Equation of one variable 
Solve the following equation.
  $$(8-x)\cdot(x^2-2x+16)^2+2x^4\cdot(x^2-2x+16)=16x^7,$$
  where $x\in \mathbb{R}$

I already know that we need to prove $x=2$, but don't know how to show it...
I'd be grateful for some hints or solutions ;)

It's $$(x-2)(16x^6+30x^5+65x^4+86x^3+240x^2+128x+1024)=0$$
and since
$$16x^6+30x^5+65x^4+86x^3+240x^2+128x+1024=$$
$$=(16x^6+30x^5+15x^4)+(50x^4+86x^3+37x^2)+(203x^2+128x+1024)>0,$$
we get the answer: $\{2\}$.
