Answer
$\{\pm\sqrt 3, \pm i\sqrt 5\}$
Work Step by Step
Step 1. Let $u=x^2$, we have $u^2+2u-15=0$
Step 2. Factor and solve: $(u+5)(u-3)=0$ thus $u=-5, 3$
Step 3. For $u=-5$, we have $x^2=-5$ and $x=\pm i\sqrt 5$
Step 4. For $u=3$, we have $x^2=3$ and $x=\pm\sqrt 3$
Step 5. Solution set $\{\pm\sqrt 3, \pm i\sqrt 5\}$