Answer
$r=\frac{-5\pm\sqrt{41}}{2}$
Work Step by Step
$\frac{1}{r}+\frac{2}{1-r}=\frac{4}{r^2}$ (Multiply by $r^2(1-r)$)
$r(1-r)+2r^2=4(1-r)$ (Simplify)
$r-r^2+2r^2=4-4r$
$r^2+r=4-4r$
$r^2+5r-4=0$ (Use the quadratic formula)
$r=\frac{-5\pm \sqrt{5^2-4\cdot 1\cdot (-4)}}{2\cdot 1}$
$r=\frac{-5\pm\sqrt{41}}{2}$
