Answer
See below
Work Step by Step
$$f(x)=x^4-x^3-5x^2-x-6=0\\x^4+2x^3-3x^3-6x^2+x^2+2x-3x-6=0\\x^3(x+2)-3x^2(x+2)+x(x+2)-3(x+2)=0\\(x+2)(x^3-3x^2+x-3)=0\\(x+2)(x-3)(x^2+1)=0$$
The solutions are $x+2=0\rightarrow x=-2\\x-3=0 \rightarrow x=3$
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