Answer
$$x=0,\:x=3,\:x=-7,\:x=-1+2\sqrt{2},\:x=-1-2\sqrt{2}$$
Work Step by Step
Factoring the equation (as necessary) and setting the factors equal to zero, we find:
$$\left(x^2+2x-7\right)\left(x^3+4x^2-21x\right) \\ x\left(x-3\right)\left(x+7\right)\left(x^2+2x-7\right) \\ x=0,\:x=3,\:x=-7,\:x=-1+2\sqrt{2},\:x=-1-2\sqrt{2}$$