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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