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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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