(x+3)(x-2+4i)(x+2+4i)=0

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Solution for (x+3)(x-2+4i)(x+2+4i)=0 equation: 


Simplifying
(x + 3)(x + -2 + 4i)(x + 2 + 4i) = 0

Reorder the terms:
(3 + x)(x + -2 + 4i)(x + 2 + 4i) = 0

Reorder the terms:
(3 + x)(-2 + 4i + x)(x + 2 + 4i) = 0

Reorder the terms:
(3 + x)(-2 + 4i + x)(2 + 4i + x) = 0

Multiply (3 + x) * (-2 + 4i + x)
(3(-2 + 4i + x) + x(-2 + 4i + x))(2 + 4i + x) = 0
((-2 * 3 + 4i * 3 + x * 3) + x(-2 + 4i + x))(2 + 4i + x) = 0
((-6 + 12i + 3x) + x(-2 + 4i + x))(2 + 4i + x) = 0
(-6 + 12i + 3x + (-2 * x + 4i * x + x * x))(2 + 4i + x) = 0

Reorder the terms:
(-6 + 12i + 3x + (4ix + -2x + x2))(2 + 4i + x) = 0
(-6 + 12i + 3x + (4ix + -2x + x2))(2 + 4i + x) = 0

Reorder the terms:
(-6 + 12i + 4ix + 3x + -2x + x2)(2 + 4i + x) = 0

Combine like terms: 3x + -2x = 1x
(-6 + 12i + 4ix + 1x + x2)(2 + 4i + x) = 0

Multiply (-6 + 12i + 4ix + 1x + x2) * (2 + 4i + x)
(-6(2 + 4i + x) + 12i * (2 + 4i + x) + 4ix * (2 + 4i + x) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0
((2 * -6 + 4i * -6 + x * -6) + 12i * (2 + 4i + x) + 4ix * (2 + 4i + x) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0
((-12 + -24i + -6x) + 12i * (2 + 4i + x) + 4ix * (2 + 4i + x) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0
(-12 + -24i + -6x + (2 * 12i + 4i * 12i + x * 12i) + 4ix * (2 + 4i + x) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0

Reorder the terms:
(-12 + -24i + -6x + (24i + 12ix + 48i2) + 4ix * (2 + 4i + x) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0
(-12 + -24i + -6x + (24i + 12ix + 48i2) + 4ix * (2 + 4i + x) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0
(-12 + -24i + -6x + 24i + 12ix + 48i2 + (2 * 4ix + 4i * 4ix + x * 4ix) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0

Reorder the terms:
(-12 + -24i + -6x + 24i + 12ix + 48i2 + (8ix + 4ix2 + 16i2x) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0
(-12 + -24i + -6x + 24i + 12ix + 48i2 + (8ix + 4ix2 + 16i2x) + 1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0
(-12 + -24i + -6x + 24i + 12ix + 48i2 + 8ix + 4ix2 + 16i2x + (2 * 1x + 4i * 1x + x * 1x) + x2(2 + 4i + x)) = 0

Reorder the terms:
(-12 + -24i + -6x + 24i + 12ix + 48i2 + 8ix + 4ix2 + 16i2x + (4ix + 2x + 1x2) + x2(2 + 4i + x)) = 0
(-12 + -24i + -6x + 24i + 12ix + 48i2 + 8ix + 4ix2 + 16i2x + (4ix + 2x + 1x2) + x2(2 + 4i + x)) = 0
(-12 + -24i + -6x + 24i + 12ix + 48i2 + 8ix + 4ix2 + 16i2x + 4ix + 2x + 1x2 + (2 * x2 + 4i * x2 + x * x2)) = 0

Reorder the terms:
(-12 + -24i + -6x + 24i + 12ix + 48i2 + 8ix + 4ix2 + 16i2x + 4ix + 2x + 1x2 + (4ix2 + 2x2 + x3)) = 0
(-12 + -24i + -6x + 24i + 12ix + 48i2 + 8ix + 4ix2 + 16i2x + 4ix + 2x + 1x2 + (4ix2 + 2x2 + x3)) = 0

Reorder the terms:
(-12 + -24i + 24i + 12ix + 8ix + 4ix + 4ix2 + 4ix2 + 48i2 + 16i2x + -6x + 2x + 1x2 + 2x2 + x3) = 0

Combine like terms: -24i + 24i = 0
(-12 + 0 + 12ix + 8ix + 4ix + 4ix2 + 4ix2 + 48i2 + 16i2x + -6x + 2x + 1x2 + 2x2 + x3) = 0
(-12 + 12ix + 8ix + 4ix + 4ix2 + 4ix2 + 48i2 + 16i2x + -6x + 2x + 1x2 + 2x2 + x3) = 0

Combine like terms: 12ix + 8ix = 20ix
(-12 + 20ix + 4ix + 4ix2 + 4ix2 + 48i2 + 16i2x + -6x + 2x + 1x2 + 2x2 + x3) = 0

Combine like terms: 20ix + 4ix = 24ix
(-12 + 24ix + 4ix2 + 4ix2 + 48i2 + 16i2x + -6x + 2x + 1x2 + 2x2 + x3) = 0

Combine like terms: 4ix2 + 4ix2 = 8ix2
(-12 + 24ix + 8ix2 + 48i2 + 16i2x + -6x + 2x + 1x2 + 2x2 + x3) = 0

Combine like terms: -6x + 2x = -4x
(-12 + 24ix + 8ix2 + 48i2 + 16i2x + -4x + 1x2 + 2x2 + x3) = 0

Combine like terms: 1x2 + 2x2 = 3x2
(-12 + 24ix + 8ix2 + 48i2 + 16i2x + -4x + 3x2 + x3) = 0

Solving
-12 + 24ix + 8ix2 + 48i2 + 16i2x + -4x + 3x2 + x3 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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