Answer
$x=\pm 1$
Work Step by Step
We solve by factoring:
$3x^{4}-2x^{2}-1=0$
$(3x^{2}+1)(x^{2}-1)=0$
$3x^{2}+1=0$ or $x^{2}-1=0$
$3x^{2}=-1$ or $x^{2}=1$
$x^2=\frac{-1}{3}$ or $x=\pm\sqrt{1}$
$x=\pm \sqrt{\frac{-1}{3}}$=not real or $x=\pm 1$
$x=\pm 1$
We ignore the unreal solution.