Proving that an equation has only a fixed point

Question

I only need a hint to solve this problem: Show that the equation $x^4+8x^3+32x-32=0$ has only a fixed point at the interval $[0,1]$. I know that as $\mathbb{R}$ is complete with the usual metric and $[0,1]$ is a closed subset then it's complete too, so now I only have to prove that the equation is a contraction so that by a theorem then the equation will have only a fixed point. My question is: how do I prove that an equation is a contraction? I only know the definition of contraction for functions. Should I write $f(x)=x^4+8x^3+32x-32$? If it's so explain why, please.