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

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


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

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

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

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

Multiply (2 + x) * (-2 + -1i + x)
(2(-2 + -1i + x) + x(-2 + -1i + x))(-2 + i + x) = 0
((-2 * 2 + -1i * 2 + x * 2) + x(-2 + -1i + x))(-2 + i + x) = 0
((-4 + -2i + 2x) + x(-2 + -1i + x))(-2 + i + x) = 0
(-4 + -2i + 2x + (-2 * x + -1i * x + x * x))(-2 + i + x) = 0

Reorder the terms:
(-4 + -2i + 2x + (-1ix + -2x + x2))(-2 + i + x) = 0
(-4 + -2i + 2x + (-1ix + -2x + x2))(-2 + i + x) = 0

Reorder the terms:
(-4 + -2i + -1ix + 2x + -2x + x2)(-2 + i + x) = 0

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

Multiply (-4 + -2i + -1ix + x2) * (-2 + i + x)
(-4(-2 + i + x) + -2i * (-2 + i + x) + -1ix * (-2 + i + x) + x2(-2 + i + x)) = 0
((-2 * -4 + i * -4 + x * -4) + -2i * (-2 + i + x) + -1ix * (-2 + i + x) + x2(-2 + i + x)) = 0
((8 + -4i + -4x) + -2i * (-2 + i + x) + -1ix * (-2 + i + x) + x2(-2 + i + x)) = 0
(8 + -4i + -4x + (-2 * -2i + i * -2i + x * -2i) + -1ix * (-2 + i + x) + x2(-2 + i + x)) = 0

Reorder the terms:
(8 + -4i + -4x + (4i + -2ix + -2i2) + -1ix * (-2 + i + x) + x2(-2 + i + x)) = 0
(8 + -4i + -4x + (4i + -2ix + -2i2) + -1ix * (-2 + i + x) + x2(-2 + i + x)) = 0
(8 + -4i + -4x + 4i + -2ix + -2i2 + (-2 * -1ix + i * -1ix + x * -1ix) + x2(-2 + i + x)) = 0

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

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

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

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

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

Combine like terms: -1ix2 + ix2 = 0
(8 + 0 + -2i2 + -1i2x + -4x + -2x2 + x3) = 0
(8 + -2i2 + -1i2x + -4x + -2x2 + x3) = 0

Solving
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -2i2 + -1i2x + -4x + -2x2 + -8 + x3 = 0 + -8

Reorder the terms:
8 + -8 + -2i2 + -1i2x + -4x + -2x2 + x3 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -2i2 + -1i2x + -4x + -2x2 + x3 = 0 + -8
-2i2 + -1i2x + -4x + -2x2 + x3 = 0 + -8

Combine like terms: 0 + -8 = -8
-2i2 + -1i2x + -4x + -2x2 + x3 = -8

Add '4x' to each side of the equation.
-2i2 + -1i2x + -4x + -2x2 + 4x + x3 = -8 + 4x

Reorder the terms:
-2i2 + -1i2x + -4x + 4x + -2x2 + x3 = -8 + 4x

Combine like terms: -4x + 4x = 0
-2i2 + -1i2x + 0 + -2x2 + x3 = -8 + 4x
-2i2 + -1i2x + -2x2 + x3 = -8 + 4x

Add '2x2' to each side of the equation.
-2i2 + -1i2x + -2x2 + 2x2 + x3 = -8 + 4x + 2x2

Combine like terms: -2x2 + 2x2 = 0
-2i2 + -1i2x + 0 + x3 = -8 + 4x + 2x2
-2i2 + -1i2x + x3 = -8 + 4x + 2x2

Add '-1x3' to each side of the equation.
-2i2 + -1i2x + x3 + -1x3 = -8 + 4x + 2x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-2i2 + -1i2x + 0 = -8 + 4x + 2x2 + -1x3
-2i2 + -1i2x = -8 + 4x + 2x2 + -1x3

Reorder the terms:
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = -8 + 4x + 2x2 + -1x3 + 8 + -4x + -2x2 + x3

Reorder the terms:
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = -8 + 8 + 4x + -4x + 2x2 + -2x2 + -1x3 + x3

Combine like terms: -8 + 8 = 0
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = 0 + 4x + -4x + 2x2 + -2x2 + -1x3 + x3
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = 4x + -4x + 2x2 + -2x2 + -1x3 + x3

Combine like terms: 4x + -4x = 0
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = 0 + 2x2 + -2x2 + -1x3 + x3
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = 2x2 + -2x2 + -1x3 + x3

Combine like terms: 2x2 + -2x2 = 0
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = 0 + -1x3 + x3
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
8 + -2i2 + -1i2x + -4x + -2x2 + x3 = 0

The solution to this equation could not be determined.

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