(x-2)(x-(1+3i))(x+(1+3i))=P(x)

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Solution for (x-2)(x-(1+3i))(x+(1+3i))=P(x) equation: 


Simplifying
(x + -2)(x + -1(1 + 3i))(x + (1 + 3i)) = P(x)

Reorder the terms:
(-2 + x)(x + -1(1 + 3i))(x + (1 + 3i)) = P(x)
(-2 + x)(x + (1 * -1 + 3i * -1))(x + (1 + 3i)) = P(x)
(-2 + x)(x + (-1 + -3i))(x + (1 + 3i)) = P(x)

Reorder the terms:
(-2 + x)(-1 + -3i + x)(x + (1 + 3i)) = P(x)

Remove parenthesis around (1 + 3i)
(-2 + x)(-1 + -3i + x)(x + 1 + 3i) = P(x)

Reorder the terms:
(-2 + x)(-1 + -3i + x)(1 + 3i + x) = P(x)

Multiply (-2 + x) * (-1 + -3i + x)
(-2(-1 + -3i + x) + x(-1 + -3i + x))(1 + 3i + x) = P(x)
((-1 * -2 + -3i * -2 + x * -2) + x(-1 + -3i + x))(1 + 3i + x) = P(x)
((2 + 6i + -2x) + x(-1 + -3i + x))(1 + 3i + x) = P(x)
(2 + 6i + -2x + (-1 * x + -3i * x + x * x))(1 + 3i + x) = P(x)

Reorder the terms:
(2 + 6i + -2x + (-3ix + -1x + x2))(1 + 3i + x) = P(x)
(2 + 6i + -2x + (-3ix + -1x + x2))(1 + 3i + x) = P(x)

Reorder the terms:
(2 + 6i + -3ix + -2x + -1x + x2)(1 + 3i + x) = P(x)

Combine like terms: -2x + -1x = -3x
(2 + 6i + -3ix + -3x + x2)(1 + 3i + x) = P(x)

Multiply (2 + 6i + -3ix + -3x + x2) * (1 + 3i + x)
(2(1 + 3i + x) + 6i * (1 + 3i + x) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)
((1 * 2 + 3i * 2 + x * 2) + 6i * (1 + 3i + x) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)
((2 + 6i + 2x) + 6i * (1 + 3i + x) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)
(2 + 6i + 2x + (1 * 6i + 3i * 6i + x * 6i) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)

Reorder the terms:
(2 + 6i + 2x + (6i + 6ix + 18i2) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)
(2 + 6i + 2x + (6i + 6ix + 18i2) + -3ix * (1 + 3i + x) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)
(2 + 6i + 2x + 6i + 6ix + 18i2 + (1 * -3ix + 3i * -3ix + x * -3ix) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)

Reorder the terms:
(2 + 6i + 2x + 6i + 6ix + 18i2 + (-3ix + -3ix2 + -9i2x) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)
(2 + 6i + 2x + 6i + 6ix + 18i2 + (-3ix + -3ix2 + -9i2x) + -3x * (1 + 3i + x) + x2(1 + 3i + x)) = P(x)
(2 + 6i + 2x + 6i + 6ix + 18i2 + -3ix + -3ix2 + -9i2x + (1 * -3x + 3i * -3x + x * -3x) + x2(1 + 3i + x)) = P(x)

Reorder the terms:
(2 + 6i + 2x + 6i + 6ix + 18i2 + -3ix + -3ix2 + -9i2x + (-9ix + -3x + -3x2) + x2(1 + 3i + x)) = P(x)
(2 + 6i + 2x + 6i + 6ix + 18i2 + -3ix + -3ix2 + -9i2x + (-9ix + -3x + -3x2) + x2(1 + 3i + x)) = P(x)
(2 + 6i + 2x + 6i + 6ix + 18i2 + -3ix + -3ix2 + -9i2x + -9ix + -3x + -3x2 + (1 * x2 + 3i * x2 + x * x2)) = P(x)

Reorder the terms:
(2 + 6i + 2x + 6i + 6ix + 18i2 + -3ix + -3ix2 + -9i2x + -9ix + -3x + -3x2 + (3ix2 + 1x2 + x3)) = P(x)
(2 + 6i + 2x + 6i + 6ix + 18i2 + -3ix + -3ix2 + -9i2x + -9ix + -3x + -3x2 + (3ix2 + 1x2 + x3)) = P(x)

Reorder the terms:
(2 + 6i + 6i + 6ix + -3ix + -9ix + -3ix2 + 3ix2 + 18i2 + -9i2x + 2x + -3x + -3x2 + 1x2 + x3) = P(x)

Combine like terms: 6i + 6i = 12i
(2 + 12i + 6ix + -3ix + -9ix + -3ix2 + 3ix2 + 18i2 + -9i2x + 2x + -3x + -3x2 + 1x2 + x3) = P(x)

Combine like terms: 6ix + -3ix = 3ix
(2 + 12i + 3ix + -9ix + -3ix2 + 3ix2 + 18i2 + -9i2x + 2x + -3x + -3x2 + 1x2 + x3) = P(x)

Combine like terms: 3ix + -9ix = -6ix
(2 + 12i + -6ix + -3ix2 + 3ix2 + 18i2 + -9i2x + 2x + -3x + -3x2 + 1x2 + x3) = P(x)

Combine like terms: -3ix2 + 3ix2 = 0
(2 + 12i + -6ix + 0 + 18i2 + -9i2x + 2x + -3x + -3x2 + 1x2 + x3) = P(x)
(2 + 12i + -6ix + 18i2 + -9i2x + 2x + -3x + -3x2 + 1x2 + x3) = P(x)

Combine like terms: 2x + -3x = -1x
(2 + 12i + -6ix + 18i2 + -9i2x + -1x + -3x2 + 1x2 + x3) = P(x)

Combine like terms: -3x2 + 1x2 = -2x2
(2 + 12i + -6ix + 18i2 + -9i2x + -1x + -2x2 + x3) = P(x)

Multiply P * x
2 + 12i + -6ix + 18i2 + -9i2x + -1x + -2x2 + x3 = xP

Solving
2 + 12i + -6ix + 18i2 + -9i2x + -1x + -2x2 + x3 = xP

Solving for variable 'i'.

Reorder the terms:
2 + 12i + -6ix + 18i2 + -9i2x + -1x + -1xP + -2x2 + x3 = xP + -1xP

Combine like terms: xP + -1xP = 0
2 + 12i + -6ix + 18i2 + -9i2x + -1x + -1xP + -2x2 + x3 = 0

The solution to this equation could not be determined.

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