Answer
See below
Work Step by Step
$$f(x)=x^3-4x^2-7x+10=0\\x^3-4x^2-7x+10=0\\x^3-x^2-3x^2+7x-10x+10=0\\x^2(x-1)-3x(x-1)-10(x-1)=0\\(x-1)(x^2-3x-10)=0\\(x-1)(x-5)(x+2)=0\\x=5 \lor x=1 \lor x=-2$$
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