X to the fourth power minus x to the third power plus 2x to the second power minus 4x minus

8=0

Regroup:

(x^4+2x^2-8) - (x^3+4x) = 0

Factor: (x^2-2) (x^2+4) - x (x^2+4) = 0

both terms have (x^2+4), so (x^2+4) (X^2-x-2) = 0

factor again: (x^2+4) (x+1) (x-2) = 0

x=1, x=2, x=2i, or x=-2i