Answer
$x=1$ or $x=-1$ or $x=-4$
Work Step by Step
We solve by factoring with grouping:
$x^{3}+4x^{2}-x-4=0$
$x^{2}(x+4)-1(x+4)=0$
$(x^{2}-1)(x+4)=0$
$(x-1)(x+1)(x+4)=0$
$x-1=0$ or $x+1=0$ or $x+4=0$
$x=1$ or $x=-1$ or $x=-4$
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