x⁴ + 4x³ + 4x² = -16x
x⁴ + 4x³ + 4x² + 16x = -16x + 16x
x⁴ + 4x³ + 4x² + 16x = 0
x(x³) + x(4x²) + x(4x) + x(16) = 0
x(x³ + 4x² + 4x + 16) = 0
x(x²(x) + x²(4) + 4(x) + 4(4)) = 0
x(x²(x + 4) + 4(x + 4)) = 0
x(x² + 4)(x + 4) = 0
x = 0 U x² + 4 = 0 U x + 4 = 0
- 4 - 4 - 4 - 4
x² = -4 x = -4
x = +2i
The solution set is equal to {-4, -2i, 0, 2i}.
