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

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


Simplifying
(x + 4)(x + -1[3 + 2i])(x + [3 + 2i]) = 0

Reorder the terms:
(4 + x)(x + -1[3 + 2i])(x + [3 + 2i]) = 0
(4 + x)(x + [3 * -1 + 2i * -1])(x + [3 + 2i]) = 0
(4 + x)(x + [-3 + -2i])(x + [3 + 2i]) = 0

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

Remove brackets around [3 + 2i]
(4 + x)(-3 + -2i + x)(x + 3 + 2i) = 0

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

Multiply (4 + x) * (-3 + -2i + x)
(4(-3 + -2i + x) + x(-3 + -2i + x))(3 + 2i + x) = 0
((-3 * 4 + -2i * 4 + x * 4) + x(-3 + -2i + x))(3 + 2i + x) = 0
((-12 + -8i + 4x) + x(-3 + -2i + x))(3 + 2i + x) = 0
(-12 + -8i + 4x + (-3 * x + -2i * x + x * x))(3 + 2i + x) = 0

Reorder the terms:
(-12 + -8i + 4x + (-2ix + -3x + x2))(3 + 2i + x) = 0
(-12 + -8i + 4x + (-2ix + -3x + x2))(3 + 2i + x) = 0

Reorder the terms:
(-12 + -8i + -2ix + 4x + -3x + x2)(3 + 2i + x) = 0

Combine like terms: 4x + -3x = 1x
(-12 + -8i + -2ix + 1x + x2)(3 + 2i + x) = 0

Multiply (-12 + -8i + -2ix + 1x + x2) * (3 + 2i + x)
(-12(3 + 2i + x) + -8i * (3 + 2i + x) + -2ix * (3 + 2i + x) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0
((3 * -12 + 2i * -12 + x * -12) + -8i * (3 + 2i + x) + -2ix * (3 + 2i + x) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0
((-36 + -24i + -12x) + -8i * (3 + 2i + x) + -2ix * (3 + 2i + x) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0
(-36 + -24i + -12x + (3 * -8i + 2i * -8i + x * -8i) + -2ix * (3 + 2i + x) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0

Reorder the terms:
(-36 + -24i + -12x + (-24i + -8ix + -16i2) + -2ix * (3 + 2i + x) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0
(-36 + -24i + -12x + (-24i + -8ix + -16i2) + -2ix * (3 + 2i + x) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0
(-36 + -24i + -12x + -24i + -8ix + -16i2 + (3 * -2ix + 2i * -2ix + x * -2ix) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0

Reorder the terms:
(-36 + -24i + -12x + -24i + -8ix + -16i2 + (-6ix + -2ix2 + -4i2x) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0
(-36 + -24i + -12x + -24i + -8ix + -16i2 + (-6ix + -2ix2 + -4i2x) + 1x * (3 + 2i + x) + x2(3 + 2i + x)) = 0
(-36 + -24i + -12x + -24i + -8ix + -16i2 + -6ix + -2ix2 + -4i2x + (3 * 1x + 2i * 1x + x * 1x) + x2(3 + 2i + x)) = 0

Reorder the terms:
(-36 + -24i + -12x + -24i + -8ix + -16i2 + -6ix + -2ix2 + -4i2x + (2ix + 3x + 1x2) + x2(3 + 2i + x)) = 0
(-36 + -24i + -12x + -24i + -8ix + -16i2 + -6ix + -2ix2 + -4i2x + (2ix + 3x + 1x2) + x2(3 + 2i + x)) = 0
(-36 + -24i + -12x + -24i + -8ix + -16i2 + -6ix + -2ix2 + -4i2x + 2ix + 3x + 1x2 + (3 * x2 + 2i * x2 + x * x2)) = 0

Reorder the terms:
(-36 + -24i + -12x + -24i + -8ix + -16i2 + -6ix + -2ix2 + -4i2x + 2ix + 3x + 1x2 + (2ix2 + 3x2 + x3)) = 0
(-36 + -24i + -12x + -24i + -8ix + -16i2 + -6ix + -2ix2 + -4i2x + 2ix + 3x + 1x2 + (2ix2 + 3x2 + x3)) = 0

Reorder the terms:
(-36 + -24i + -24i + -8ix + -6ix + 2ix + -2ix2 + 2ix2 + -16i2 + -4i2x + -12x + 3x + 1x2 + 3x2 + x3) = 0

Combine like terms: -24i + -24i = -48i
(-36 + -48i + -8ix + -6ix + 2ix + -2ix2 + 2ix2 + -16i2 + -4i2x + -12x + 3x + 1x2 + 3x2 + x3) = 0

Combine like terms: -8ix + -6ix = -14ix
(-36 + -48i + -14ix + 2ix + -2ix2 + 2ix2 + -16i2 + -4i2x + -12x + 3x + 1x2 + 3x2 + x3) = 0

Combine like terms: -14ix + 2ix = -12ix
(-36 + -48i + -12ix + -2ix2 + 2ix2 + -16i2 + -4i2x + -12x + 3x + 1x2 + 3x2 + x3) = 0

Combine like terms: -2ix2 + 2ix2 = 0
(-36 + -48i + -12ix + 0 + -16i2 + -4i2x + -12x + 3x + 1x2 + 3x2 + x3) = 0
(-36 + -48i + -12ix + -16i2 + -4i2x + -12x + 3x + 1x2 + 3x2 + x3) = 0

Combine like terms: -12x + 3x = -9x
(-36 + -48i + -12ix + -16i2 + -4i2x + -9x + 1x2 + 3x2 + x3) = 0

Combine like terms: 1x2 + 3x2 = 4x2
(-36 + -48i + -12ix + -16i2 + -4i2x + -9x + 4x2 + x3) = 0

Solving
-36 + -48i + -12ix + -16i2 + -4i2x + -9x + 4x2 + x3 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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