Polynomial equations with Even Powers Only

If $P(x)$ has degree $2n$ and involves only even powers of $x$ (every odd-power coefficient is $0$), substitute $y=x^2$: this turns $P(x)=0$ into a genuine degree-$n$ equation in $y$. Solve for the roots $y_1,\ldots,y_n$, then for each $y_r$ solve $x^2=y_r$ to recover (up to) two $x$-values — giving up to $2n$ roots of the original equation in total, exactly matching its degree.

Worked illustration (Example 3.16). $x^4-9x^2+20=0$: with $y=x^2$, $y^2-9y+20=0=(y-4)(y-5)$, so $y=4$ or $y=5$. Then $x^2=4\Rightarrow x=\pm2$ and $x^2=5\Rightarrow x=\pm\sqrt5$; the four roots are $2,-2,\sqrt5,-\sqrt5$. …