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

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Solution for x=(x+1+2i)(x+1-2i) equation: 


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

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

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

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

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

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

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

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

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

Combine like terms: 1x + 1x = 2x
x = (1 + -4i2 + 2x + x2)

Solving
x = 1 + -4i2 + 2x + x2

Solving for variable 'x'.

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

Combine like terms: x + -2x = -1x
-1 + 4i2 + -1x + -1x2 = 1 + -4i2 + 2x + x2 + -1 + 4i2 + -2x + -1x2

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

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

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

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

Combine like terms: x2 + -1x2 = 0
-1 + 4i2 + -1x + -1x2 = 0

The solution to this equation could not be determined.

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