Solve for x

Solve x^3(x^2 - 5) = -4x

 

x^3(x^2 - 5) = -4x
x^5 - 5x^3 = -4x
x^5 - 5x^3 +4x=0
(x^4 - 5x^2 +4)x=0

=> one solution is x=0

x^4 - 5x^2 +4=0 ...........factor
x^4 - x^2 -4x^2+4=0
(x^4 - x^2) -(4x^2-4)=0
x^2(x^2 - 1) -4(x^2-1)=0
(x^2-4)(x^2-1)=0
(x^2-2^2)(x^2-1)=0
(x - 2) (x + 2) (x - 1) (x + 1)= 0

=> other solutions are x=2, x=-2, x=1, x=-1

combine solutions: x=0, x=2, x=-2, x=1, x=-1

 

This one is a nasty problem.