0=(x+3)(x+3)(x+3+2i)(x+3+2i)

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Solution for 0=(x+3)(x+3)(x+3+2i)(x+3+2i) equation:

Simplifying
0 = (x + 3)(x + 3)(x + 3 + 2i)(x + 3 + 2i)

Reorder the terms:
0 = (3 + x)(x + 3)(x + 3 + 2i)(x + 3 + 2i)

Reorder the terms:
0 = (3 + x)(3 + x)(x + 3 + 2i)(x + 3 + 2i)

Reorder the terms:
0 = (3 + x)(3 + x)(3 + 2i + x)(x + 3 + 2i)

Reorder the terms:
0 = (3 + x)(3 + x)(3 + 2i + x)(3 + 2i + x)

Multiply (3 + x) * (3 + x)
0 = (3(3 + x) + x(3 + x))(3 + 2i + x)(3 + 2i + x)
0 = ((3 * 3 + x * 3) + x(3 + x))(3 + 2i + x)(3 + 2i + x)
0 = ((9 + 3x) + x(3 + x))(3 + 2i + x)(3 + 2i + x)
0 = (9 + 3x + (3 * x + x * x))(3 + 2i + x)(3 + 2i + x)
0 = (9 + 3x + (3x + x²))(3 + 2i + x)(3 + 2i + x)

Combine like terms: 3x + 3x = 6x
0 = (9 + 6x + x²)(3 + 2i + x)(3 + 2i + x)

Multiply (9 + 6x + x²) * (3 + 2i + x)
0 = (9(3 + 2i + x) + 6x * (3 + 2i + x) + x²(3 + 2i + x))(3 + 2i + x)
0 = ((3 * 9 + 2i * 9 + x * 9) + 6x * (3 + 2i + x) + x²(3 + 2i + x))(3 + 2i + x)
0 = ((27 + 18i + 9x) + 6x * (3 + 2i + x) + x²(3 + 2i + x))(3 + 2i + x)
0 = (27 + 18i + 9x + (3 * 6x + 2i * 6x + x * 6x) + x²(3 + 2i + x))(3 + 2i + x)

Reorder the terms:
0 = (27 + 18i + 9x + (12ix + 18x + 6x²) + x²(3 + 2i + x))(3 + 2i + x)
0 = (27 + 18i + 9x + (12ix + 18x + 6x²) + x²(3 + 2i + x))(3 + 2i + x)
0 = (27 + 18i + 9x + 12ix + 18x + 6x² + (3 * x² + 2i * x² + x * x²))(3 + 2i + x)

Reorder the terms:
0 = (27 + 18i + 9x + 12ix + 18x + 6x² + (2ix² + 3x² + x³))(3 + 2i + x)
0 = (27 + 18i + 9x + 12ix + 18x + 6x² + (2ix² + 3x² + x³))(3 + 2i + x)

Reorder the terms:
0 = (27 + 18i + 12ix + 2ix² + 9x + 18x + 6x² + 3x² + x³)(3 + 2i + x)

Combine like terms: 9x + 18x = 27x
0 = (27 + 18i + 12ix + 2ix² + 27x + 6x² + 3x² + x³)(3 + 2i + x)

Combine like terms: 6x² + 3x² = 9x²
0 = (27 + 18i + 12ix + 2ix² + 27x + 9x² + x³)(3 + 2i + x)

Multiply (27 + 18i + 12ix + 2ix² + 27x + 9x² + x³) * (3 + 2i + x)
0 = (27(3 + 2i + x) + 18i * (3 + 2i + x) + 12ix * (3 + 2i + x) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = ((3 * 27 + 2i * 27 + x * 27) + 18i * (3 + 2i + x) + 12ix * (3 + 2i + x) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = ((81 + 54i + 27x) + 18i * (3 + 2i + x) + 12ix * (3 + 2i + x) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + (3 * 18i + 2i * 18i + x * 18i) + 12ix * (3 + 2i + x) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))

Reorder the terms:
0 = (81 + 54i + 27x + (54i + 18ix + 36i²) + 12ix * (3 + 2i + x) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + (54i + 18ix + 36i²) + 12ix * (3 + 2i + x) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + (3 * 12ix + 2i * 12ix + x * 12ix) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))

Reorder the terms:
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + (36ix + 12ix² + 24i²x) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + (36ix + 12ix² + 24i²x) + 2ix² * (3 + 2i + x) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + (3 * 2ix² + 2i * 2ix² + x * 2ix²) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))

Reorder the terms:
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + (6ix² + 2ix³ + 4i²x²) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + (6ix² + 2ix³ + 4i²x²) + 27x * (3 + 2i + x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + (3 * 27x + 2i * 27x + x * 27x) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))

Reorder the terms:
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + (54ix + 81x + 27x²) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + (54ix + 81x + 27x²) + 9x² * (3 + 2i + x) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + 54ix + 81x + 27x² + (3 * 9x² + 2i * 9x² + x * 9x²) + x³(3 + 2i + x))

Reorder the terms:
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + 54ix + 81x + 27x² + (18ix² + 27x² + 9x³) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + 54ix + 81x + 27x² + (18ix² + 27x² + 9x³) + x³(3 + 2i + x))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + 54ix + 81x + 27x² + 18ix² + 27x² + 9x³ + (3 * x³ + 2i * x³ + x * x³))

Reorder the terms:
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + 54ix + 81x + 27x² + 18ix² + 27x² + 9x³ + (2ix³ + 3x³ + x⁴))
0 = (81 + 54i + 27x + 54i + 18ix + 36i² + 36ix + 12ix² + 24i²x + 6ix² + 2ix³ + 4i²x² + 54ix + 81x + 27x² + 18ix² + 27x² + 9x³ + (2ix³ + 3x³ + x⁴))

Reorder the terms:
0 = (81 + 54i + 54i + 18ix + 36ix + 54ix + 12ix² + 6ix² + 18ix² + 2ix³ + 2ix³ + 36i² + 24i²x + 4i²x² + 27x + 81x + 27x² + 27x² + 9x³ + 3x³ + x⁴)

Combine like terms: 54i + 54i = 108i
0 = (81 + 108i + 18ix + 36ix + 54ix + 12ix² + 6ix² + 18ix² + 2ix³ + 2ix³ + 36i² + 24i²x + 4i²x² + 27x + 81x + 27x² + 27x² + 9x³ + 3x³ + x⁴)

Combine like terms: 18ix + 36ix = 54ix
0 = (81 + 108i + 54ix + 54ix + 12ix² + 6ix² + 18ix² + 2ix³ + 2ix³ + 36i² + 24i²x + 4i²x² + 27x + 81x + 27x² + 27x² + 9x³ + 3x³ + x⁴)

Combine like terms: 54ix + 54ix = 108ix
0 = (81 + 108i + 108ix + 12ix² + 6ix² + 18ix² + 2ix³ + 2ix³ + 36i² + 24i²x + 4i²x² + 27x + 81x + 27x² + 27x² + 9x³ + 3x³ + x⁴)

Combine like terms: 12ix² + 6ix² = 18ix²
0 = (81 + 108i + 108ix + 18ix² + 18ix² + 2ix³ + 2ix³ + 36i² + 24i²x + 4i²x² + 27x + 81x + 27x² + 27x² + 9x³ + 3x³ + x⁴)

Combine like terms: 18ix² + 18ix² = 36ix²
0 = (81 + 108i + 108ix + 36ix² + 2ix³ + 2ix³ + 36i² + 24i²x + 4i²x² + 27x + 81x + 27x² + 27x² + 9x³ + 3x³ + x⁴)

Combine like terms: 2ix³ + 2ix³ = 4ix³
0 = (81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 27x + 81x + 27x² + 27x² + 9x³ + 3x³ + x⁴)

Combine like terms: 27x + 81x = 108x
0 = (81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 27x² + 27x² + 9x³ + 3x³ + x⁴)

Combine like terms: 27x² + 27x² = 54x²
0 = (81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 54x² + 9x³ + 3x³ + x⁴)

Combine like terms: 9x³ + 3x³ = 12x³
0 = (81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 54x² + 12x³ + x⁴)

Solving
0 = 81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 54x² + 12x³ + x⁴

Solving for variable 'i'.

Combine like terms: 0 + -81 = -81
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 54x² + 12x³ + x⁴ + -81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴

Reorder the terms:
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 81 + -81 + 108i + -108i + 108ix + -108ix + 36ix² + -36ix² + 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 81 + -81 = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 108i + -108i + 108ix + -108ix + 36ix² + -36ix² + 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 108i + -108i + 108ix + -108ix + 36ix² + -36ix² + 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 108i + -108i = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 108ix + -108ix + 36ix² + -36ix² + 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 108ix + -108ix + 36ix² + -36ix² + 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 108ix + -108ix = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 36ix² + -36ix² + 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 36ix² + -36ix² + 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 36ix² + -36ix² = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 4ix³ + -4ix³ + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 4ix³ + -4ix³ = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 36i² + -36i² + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 36i² + -36i² = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 24i²x + -24i²x + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 24i²x + -24i²x = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 4i²x² + -4i²x² + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 4i²x² + -4i²x² = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 108x + -108x + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 108x + -108x = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 54x² + -54x² + 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 54x² + -54x² = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + 12x³ + -12x³ + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 12x³ + -12x³ + x⁴ + -1x⁴

Combine like terms: 12x³ + -12x³ = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0 + x⁴ + -1x⁴
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = x⁴ + -1x⁴

Combine like terms: x⁴ + -1x⁴ = 0
-81 + -108i + -108ix + -36ix² + -4ix³ + -36i² + -24i²x + -4i²x² + -108x + -54x² + -12x³ + -1x⁴ = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 54x² + 12x³ + x⁴) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 54x² + 12x³ + x⁴)' equal to zero and attempt to solve:

Simplifying
81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 54x² + 12x³ + x⁴ = 0

Solving
81 + 108i + 108ix + 36ix² + 4ix³ + 36i² + 24i²x + 4i²x² + 108x + 54x² + 12x³ + x⁴ = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.
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0=(x+3)(x+3)(x+3+2i)(x+3+2i)

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Solution for 0=(x+3)(x+3)(x+3+2i)(x+3+2i) equation:

Subproblem 1

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