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

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


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

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

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

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

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

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

Multiply [-2 + -2i + x] * [-2 + 2i + x]
xP = [-2[-2 + 2i + x] + -2i * [-2 + 2i + x] + x[-2 + 2i + x]](1 + x)(-2 + x)
xP = [[-2 * -2 + 2i * -2 + x * -2] + -2i * [-2 + 2i + x] + x[-2 + 2i + x]](1 + x)(-2 + x)
xP = [[4 + -4i + -2x] + -2i * [-2 + 2i + x] + x[-2 + 2i + x]](1 + x)(-2 + x)
xP = [4 + -4i + -2x + [-2 * -2i + 2i * -2i + x * -2i] + x[-2 + 2i + x]](1 + x)(-2 + x)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
xP = -8 + 8i2 + 4i2x + -4i2x2 + 4x + 6x2 + -5x3 + x4

Solving for variable 'x'.

Reorder the terms:
8 + -8i2 + -4i2x + 4i2x2 + -4x + xP + -6x2 + 5x3 + -1x4 = -8 + 8i2 + 4i2x + -4i2x2 + 4x + 6x2 + -5x3 + x4 + 8 + -8i2 + -4i2x + 4i2x2 + -4x + -6x2 + 5x3 + -1x4

Reorder the terms:
8 + -8i2 + -4i2x + 4i2x2 + -4x + xP + -6x2 + 5x3 + -1x4 = -8 + 8 + 8i2 + -8i2 + 4i2x + -4i2x + -4i2x2 + 4i2x2 + 4x + -4x + 6x2 + -6x2 + -5x3 + 5x3 + x4 + -1x4

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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