Solve the inequality `(x+3)(3x-2)^5(7-x)^3(5x+8)^2 >= 0.`

Explanation

We have `(x+3)(3x-2)^(2)(7-x)^(2)(5x+8)^(2)ge0`
`implies-(x+3)(3x-2)^(5)(x-7)^(3)(5x+8)^(2)ge0`
`implies(x+3)(3x-2)^(5)(x-7)^(3)(5x+8)^(2)le0`
[take before `x,+ve` sign in all brackets]
The critial points are `(-3),(-8/5),2/3,7`.
Hence `x epsilon (-oo,-3)uu[2/3,7]uu{-8/5}`.