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

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Solution for 0=[x-(1+2i)][x-(1-2i)](x-1)(x+2) equation: 


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply [-1 + 4i2 + -4i2x + 3x + -3x2 + x3] * (2 + x)
0 = [-1(2 + x) + 4i2 * (2 + x) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x)]
0 = [(2 * -1 + x * -1) + 4i2 * (2 + x) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x)]
0 = [(-2 + -1x) + 4i2 * (2 + x) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x)]
0 = [-2 + -1x + (2 * 4i2 + x * 4i2) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x)]
0 = [-2 + -1x + (8i2 + 4i2x) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x)]
0 = [-2 + -1x + 8i2 + 4i2x + (2 * -4i2x + x * -4i2x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x)]
0 = [-2 + -1x + 8i2 + 4i2x + (-8i2x + -4i2x2) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x)]
0 = [-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + (2 * 3x + x * 3x) + -3x2 * (2 + x) + x3(2 + x)]
0 = [-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + (6x + 3x2) + -3x2 * (2 + x) + x3(2 + x)]
0 = [-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + 6x + 3x2 + (2 * -3x2 + x * -3x2) + x3(2 + x)]
0 = [-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + 6x + 3x2 + (-6x2 + -3x3) + x3(2 + x)]
0 = [-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + 6x + 3x2 + -6x2 + -3x3 + (2 * x3 + x * x3)]
0 = [-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + 6x + 3x2 + -6x2 + -3x3 + (2x3 + x4)]

Reorder the terms:
0 = [-2 + 8i2 + 4i2x + -8i2x + -4i2x2 + -1x + 6x + 3x2 + -6x2 + -3x3 + 2x3 + x4]

Combine like terms: 4i2x + -8i2x = -4i2x
0 = [-2 + 8i2 + -4i2x + -4i2x2 + -1x + 6x + 3x2 + -6x2 + -3x3 + 2x3 + x4]

Combine like terms: -1x + 6x = 5x
0 = [-2 + 8i2 + -4i2x + -4i2x2 + 5x + 3x2 + -6x2 + -3x3 + 2x3 + x4]

Combine like terms: 3x2 + -6x2 = -3x2
0 = [-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -3x3 + 2x3 + x4]

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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