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

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


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

Reorder the terms:
(2 + x)(x + 3)(x + -1(2 + -1i))(x + (2 + i)) = 0

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

Reorder the terms:
(2 + x)(3 + x)(-2 + 1i + x)(x + (2 + i)) = 0

Remove parenthesis around (2 + i)
(2 + x)(3 + x)(-2 + 1i + x)(x + 2 + i) = 0

Reorder the terms:
(2 + x)(3 + x)(-2 + 1i + x)(2 + i + x) = 0

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x))(-2 + 1i + x)(2 + i + x) = 0
((3 * 2 + x * 2) + x(3 + x))(-2 + 1i + x)(2 + i + x) = 0
((6 + 2x) + x(3 + x))(-2 + 1i + x)(2 + i + x) = 0
(6 + 2x + (3 * x + x * x))(-2 + 1i + x)(2 + i + x) = 0
(6 + 2x + (3x + x2))(-2 + 1i + x)(2 + i + x) = 0

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2)(-2 + 1i + x)(2 + i + x) = 0

Multiply (6 + 5x + x2) * (-2 + 1i + x)
(6(-2 + 1i + x) + 5x * (-2 + 1i + x) + x2(-2 + 1i + x))(2 + i + x) = 0
((-2 * 6 + 1i * 6 + x * 6) + 5x * (-2 + 1i + x) + x2(-2 + 1i + x))(2 + i + x) = 0
((-12 + 6i + 6x) + 5x * (-2 + 1i + x) + x2(-2 + 1i + x))(2 + i + x) = 0
(-12 + 6i + 6x + (-2 * 5x + 1i * 5x + x * 5x) + x2(-2 + 1i + x))(2 + i + x) = 0

Reorder the terms:
(-12 + 6i + 6x + (5ix + -10x + 5x2) + x2(-2 + 1i + x))(2 + i + x) = 0
(-12 + 6i + 6x + (5ix + -10x + 5x2) + x2(-2 + 1i + x))(2 + i + x) = 0
(-12 + 6i + 6x + 5ix + -10x + 5x2 + (-2 * x2 + 1i * x2 + x * x2))(2 + i + x) = 0

Reorder the terms:
(-12 + 6i + 6x + 5ix + -10x + 5x2 + (1ix2 + -2x2 + x3))(2 + i + x) = 0
(-12 + 6i + 6x + 5ix + -10x + 5x2 + (1ix2 + -2x2 + x3))(2 + i + x) = 0

Reorder the terms:
(-12 + 6i + 5ix + 1ix2 + 6x + -10x + 5x2 + -2x2 + x3)(2 + i + x) = 0

Combine like terms: 6x + -10x = -4x
(-12 + 6i + 5ix + 1ix2 + -4x + 5x2 + -2x2 + x3)(2 + i + x) = 0

Combine like terms: 5x2 + -2x2 = 3x2
(-12 + 6i + 5ix + 1ix2 + -4x + 3x2 + x3)(2 + i + x) = 0

Multiply (-12 + 6i + 5ix + 1ix2 + -4x + 3x2 + x3) * (2 + i + x)
(-12(2 + i + x) + 6i * (2 + i + x) + 5ix * (2 + i + x) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
((2 * -12 + i * -12 + x * -12) + 6i * (2 + i + x) + 5ix * (2 + i + x) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
((-24 + -12i + -12x) + 6i * (2 + i + x) + 5ix * (2 + i + x) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + (2 * 6i + i * 6i + x * 6i) + 5ix * (2 + i + x) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0

Reorder the terms:
(-24 + -12i + -12x + (12i + 6ix + 6i2) + 5ix * (2 + i + x) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + (12i + 6ix + 6i2) + 5ix * (2 + i + x) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + (2 * 5ix + i * 5ix + x * 5ix) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0

Reorder the terms:
(-24 + -12i + -12x + 12i + 6ix + 6i2 + (10ix + 5ix2 + 5i2x) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + (10ix + 5ix2 + 5i2x) + 1ix2 * (2 + i + x) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + (2 * 1ix2 + i * 1ix2 + x * 1ix2) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0

Reorder the terms:
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + (2ix2 + 1ix3 + 1i2x2) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + (2ix2 + 1ix3 + 1i2x2) + -4x * (2 + i + x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + (2 * -4x + i * -4x + x * -4x) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0

Reorder the terms:
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + (-4ix + -8x + -4x2) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + (-4ix + -8x + -4x2) + 3x2 * (2 + i + x) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + -4ix + -8x + -4x2 + (2 * 3x2 + i * 3x2 + x * 3x2) + x3(2 + i + x)) = 0

Reorder the terms:
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + -4ix + -8x + -4x2 + (3ix2 + 6x2 + 3x3) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + -4ix + -8x + -4x2 + (3ix2 + 6x2 + 3x3) + x3(2 + i + x)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + -4ix + -8x + -4x2 + 3ix2 + 6x2 + 3x3 + (2 * x3 + i * x3 + x * x3)) = 0

Reorder the terms:
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + -4ix + -8x + -4x2 + 3ix2 + 6x2 + 3x3 + (ix3 + 2x3 + x4)) = 0
(-24 + -12i + -12x + 12i + 6ix + 6i2 + 10ix + 5ix2 + 5i2x + 2ix2 + 1ix3 + 1i2x2 + -4ix + -8x + -4x2 + 3ix2 + 6x2 + 3x3 + (ix3 + 2x3 + x4)) = 0

Reorder the terms:
(-24 + -12i + 12i + 6ix + 10ix + -4ix + 5ix2 + 2ix2 + 3ix2 + 1ix3 + ix3 + 6i2 + 5i2x + 1i2x2 + -12x + -8x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: -12i + 12i = 0
(-24 + 0 + 6ix + 10ix + -4ix + 5ix2 + 2ix2 + 3ix2 + 1ix3 + ix3 + 6i2 + 5i2x + 1i2x2 + -12x + -8x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0
(-24 + 6ix + 10ix + -4ix + 5ix2 + 2ix2 + 3ix2 + 1ix3 + ix3 + 6i2 + 5i2x + 1i2x2 + -12x + -8x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: 6ix + 10ix = 16ix
(-24 + 16ix + -4ix + 5ix2 + 2ix2 + 3ix2 + 1ix3 + ix3 + 6i2 + 5i2x + 1i2x2 + -12x + -8x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: 16ix + -4ix = 12ix
(-24 + 12ix + 5ix2 + 2ix2 + 3ix2 + 1ix3 + ix3 + 6i2 + 5i2x + 1i2x2 + -12x + -8x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: 5ix2 + 2ix2 = 7ix2
(-24 + 12ix + 7ix2 + 3ix2 + 1ix3 + ix3 + 6i2 + 5i2x + 1i2x2 + -12x + -8x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: 7ix2 + 3ix2 = 10ix2
(-24 + 12ix + 10ix2 + 1ix3 + ix3 + 6i2 + 5i2x + 1i2x2 + -12x + -8x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: 1ix3 + ix3 = 2ix3
(-24 + 12ix + 10ix2 + 2ix3 + 6i2 + 5i2x + 1i2x2 + -12x + -8x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: -12x + -8x = -20x
(-24 + 12ix + 10ix2 + 2ix3 + 6i2 + 5i2x + 1i2x2 + -20x + -4x2 + 6x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: -4x2 + 6x2 = 2x2
(-24 + 12ix + 10ix2 + 2ix3 + 6i2 + 5i2x + 1i2x2 + -20x + 2x2 + 3x3 + 2x3 + x4) = 0

Combine like terms: 3x3 + 2x3 = 5x3
(-24 + 12ix + 10ix2 + 2ix3 + 6i2 + 5i2x + 1i2x2 + -20x + 2x2 + 5x3 + x4) = 0

Solving
-24 + 12ix + 10ix2 + 2ix3 + 6i2 + 5i2x + 1i2x2 + -20x + 2x2 + 5x3 + x4 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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