Using substitution $p = x + \frac{1}{x}$ to reduce $2x^4+x^3-6x^2+x+2=0$ How do I use the substitution $p = x + \frac{1}{x}$ to show that the equation
$$2x^4+x^3-6x^2+x+2=0$$
reduces to $2p^2+p-10=0$.
Now, I can do the problem in reverse, but when I try solving $p = x + \frac{1}{x}$ for $x$ and substituting, the resulting equation is too complicated and nothing like the form required. 

HINT : 
Dividing the both sides by $x^2$ gives
$$2x^2+x-6+\frac 1x+\frac{2}{x^2}=0,$$
i.e.
$$2\left(x^2+\frac{1}{x^2}\right)+\left(x+\frac 1x\right)-6=0.$$
