Answer
$x=2$ or $x=-1$
Work Step by Step
We solve by factoring:
$x^{6}-7x^{3}-8=0$
$(x^{3}-8)(x^{3}+1)=0$
$x^{3}-8=0$ or $x^{3}+1=0$
$x^{3}=8$ or $x^{3}=-1$
$x=\sqrt[3]{8}$ or $x=\sqrt[3]{-1}$
$x=2$ or $x=-1$
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