I need help with an inequality

[stn0091]

Solve the inequality.

x((1-x²)^4) + (x+3)((1-x²)^4) ≥ 0

[HallsofIvy]

Since there is a (1-x²)^4 term in each part, we can factor:
(1-x²)^4)(x+ (x+3))≥ 0 or
(1-x²)^4 (2x+3)≥ 0
Since a fourth power of any real number is greater than or equal to 0, this will be greater than or equal to 0 if and only if 2x+3≥ 0 so 2x≥ -3, x≥ -3/2.