Answer
$x=3$ or $x=1$ or $x=-1$
Work Step by Step
We solve by factoring with grouping:
$x^{3}-3x^{2}-x+3=0$
$x^{2}(x-3)-1(x-3)=0$
$(x-3)(x^{2}-1)=0$
$(x-3)(x-1)(x+1)=0$
$x-3=0$ or $x-1=0$ or $x+1=0$
$x=3$ or $x=1$ or $x=-1$
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