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

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


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

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

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

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

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

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

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

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

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

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

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

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

Multiply [1 + -4i2 + -2x + x2] * (2 + x)
[1(2 + x) + -4i2 * (2 + x) + -2x * (2 + x) + x2(2 + x)](-1 + x) = 0
[(2 * 1 + x * 1) + -4i2 * (2 + x) + -2x * (2 + x) + x2(2 + x)](-1 + x) = 0
[(2 + 1x) + -4i2 * (2 + x) + -2x * (2 + x) + x2(2 + x)](-1 + x) = 0
[2 + 1x + (2 * -4i2 + x * -4i2) + -2x * (2 + x) + x2(2 + x)](-1 + x) = 0
[2 + 1x + (-8i2 + -4i2x) + -2x * (2 + x) + x2(2 + x)](-1 + x) = 0
[2 + 1x + -8i2 + -4i2x + (2 * -2x + x * -2x) + x2(2 + x)](-1 + x) = 0
[2 + 1x + -8i2 + -4i2x + (-4x + -2x2) + x2(2 + x)](-1 + x) = 0
[2 + 1x + -8i2 + -4i2x + -4x + -2x2 + (2 * x2 + x * x2)](-1 + x) = 0
[2 + 1x + -8i2 + -4i2x + -4x + -2x2 + (2x2 + x3)](-1 + x) = 0

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

Combine like terms: 1x + -4x = -3x
[2 + -8i2 + -4i2x + -3x + -2x2 + 2x2 + x3](-1 + x) = 0

Combine like terms: -2x2 + 2x2 = 0
[2 + -8i2 + -4i2x + -3x + 0 + x3](-1 + x) = 0
[2 + -8i2 + -4i2x + -3x + x3](-1 + x) = 0

Multiply [2 + -8i2 + -4i2x + -3x + x3] * (-1 + x)
[2(-1 + x) + -8i2 * (-1 + x) + -4i2x * (-1 + x) + -3x * (-1 + x) + x3(-1 + x)] = 0
[(-1 * 2 + x * 2) + -8i2 * (-1 + x) + -4i2x * (-1 + x) + -3x * (-1 + x) + x3(-1 + x)] = 0
[(-2 + 2x) + -8i2 * (-1 + x) + -4i2x * (-1 + x) + -3x * (-1 + x) + x3(-1 + x)] = 0
[-2 + 2x + (-1 * -8i2 + x * -8i2) + -4i2x * (-1 + x) + -3x * (-1 + x) + x3(-1 + x)] = 0
[-2 + 2x + (8i2 + -8i2x) + -4i2x * (-1 + x) + -3x * (-1 + x) + x3(-1 + x)] = 0
[-2 + 2x + 8i2 + -8i2x + (-1 * -4i2x + x * -4i2x) + -3x * (-1 + x) + x3(-1 + x)] = 0
[-2 + 2x + 8i2 + -8i2x + (4i2x + -4i2x2) + -3x * (-1 + x) + x3(-1 + x)] = 0
[-2 + 2x + 8i2 + -8i2x + 4i2x + -4i2x2 + (-1 * -3x + x * -3x) + x3(-1 + x)] = 0
[-2 + 2x + 8i2 + -8i2x + 4i2x + -4i2x2 + (3x + -3x2) + x3(-1 + x)] = 0
[-2 + 2x + 8i2 + -8i2x + 4i2x + -4i2x2 + 3x + -3x2 + (-1 * x3 + x * x3)] = 0
[-2 + 2x + 8i2 + -8i2x + 4i2x + -4i2x2 + 3x + -3x2 + (-1x3 + x4)] = 0

Reorder the terms:
[-2 + 8i2 + -8i2x + 4i2x + -4i2x2 + 2x + 3x + -3x2 + -1x3 + x4] = 0

Combine like terms: -8i2x + 4i2x = -4i2x
[-2 + 8i2 + -4i2x + -4i2x2 + 2x + 3x + -3x2 + -1x3 + x4] = 0

Combine like terms: 2x + 3x = 5x
[-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4] = 0

Solving
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0

Solving for variable 'i'.

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

Add '2' to each side of the equation.
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + 2 + x4 = 0 + 2

Reorder the terms:
-2 + 2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0 + 2
8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0 + 2

Combine like terms: 0 + 2 = 2
8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 2

Add '-5x' to each side of the equation.
8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + -5x + x4 = 2 + -5x

Reorder the terms:
8i2 + -4i2x + -4i2x2 + 5x + -5x + -3x2 + -1x3 + x4 = 2 + -5x

Combine like terms: 5x + -5x = 0
8i2 + -4i2x + -4i2x2 + 0 + -3x2 + -1x3 + x4 = 2 + -5x
8i2 + -4i2x + -4i2x2 + -3x2 + -1x3 + x4 = 2 + -5x

Add '3x2' to each side of the equation.
8i2 + -4i2x + -4i2x2 + -3x2 + -1x3 + 3x2 + x4 = 2 + -5x + 3x2

Reorder the terms:
8i2 + -4i2x + -4i2x2 + -3x2 + 3x2 + -1x3 + x4 = 2 + -5x + 3x2

Combine like terms: -3x2 + 3x2 = 0
8i2 + -4i2x + -4i2x2 + 0 + -1x3 + x4 = 2 + -5x + 3x2
8i2 + -4i2x + -4i2x2 + -1x3 + x4 = 2 + -5x + 3x2

Add 'x3' to each side of the equation.
8i2 + -4i2x + -4i2x2 + -1x3 + x3 + x4 = 2 + -5x + 3x2 + x3

Combine like terms: -1x3 + x3 = 0
8i2 + -4i2x + -4i2x2 + 0 + x4 = 2 + -5x + 3x2 + x3
8i2 + -4i2x + -4i2x2 + x4 = 2 + -5x + 3x2 + x3

Add '-1x4' to each side of the equation.
8i2 + -4i2x + -4i2x2 + x4 + -1x4 = 2 + -5x + 3x2 + x3 + -1x4

Combine like terms: x4 + -1x4 = 0
8i2 + -4i2x + -4i2x2 + 0 = 2 + -5x + 3x2 + x3 + -1x4
8i2 + -4i2x + -4i2x2 = 2 + -5x + 3x2 + x3 + -1x4

Reorder the terms:
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 2 + -5x + 3x2 + x3 + -1x4 + -2 + 5x + -3x2 + -1x3 + x4

Reorder the terms:
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 2 + -2 + -5x + 5x + 3x2 + -3x2 + x3 + -1x3 + -1x4 + x4

Combine like terms: 2 + -2 = 0
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0 + -5x + 5x + 3x2 + -3x2 + x3 + -1x3 + -1x4 + x4
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = -5x + 5x + 3x2 + -3x2 + x3 + -1x3 + -1x4 + x4

Combine like terms: -5x + 5x = 0
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0 + 3x2 + -3x2 + x3 + -1x3 + -1x4 + x4
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 3x2 + -3x2 + x3 + -1x3 + -1x4 + x4

Combine like terms: 3x2 + -3x2 = 0
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0 + x3 + -1x3 + -1x4 + x4
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = x3 + -1x3 + -1x4 + x4

Combine like terms: x3 + -1x3 = 0
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0 + -1x4 + x4
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4 = 0

The solution to this equation could not be determined.

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