((x³ + 6x²)(x-4) + 21x³ + 3x - 12 - 3x + 12)/(x-4) ≤ 0
(x⁴ + 6x³ - 4x³ - 24x² + 21x³)/(x-4) ≤ 0
(x⁴ + 23x³ - 24x²)/(x-4) ≤ 0
x²(x² + 23x - 24)/(x-4) ≤ 0
x²(x+24)(x-1)/(x-4) ≤ 0
__-___[-24]___+__[0]___+___[1]___-__(4)___+__
Ответ: x∈(-∞; 24]U{0}U[1;4)