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

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


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

Multiply f * x
fx = (x + -1 + 3i)(x + -1 + 3i)(x + -2)(x + 1)

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

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

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

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

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

Reorder the terms:
fx = (1 + -3i + -1x + (-3i + 3ix + 9i2) + x(-1 + 3i + x))(-2 + x)(1 + x)
fx = (1 + -3i + -1x + (-3i + 3ix + 9i2) + x(-1 + 3i + x))(-2 + x)(1 + x)
fx = (1 + -3i + -1x + -3i + 3ix + 9i2 + (-1 * x + 3i * x + x * x))(-2 + x)(1 + x)

Reorder the terms:
fx = (1 + -3i + -1x + -3i + 3ix + 9i2 + (3ix + -1x + x2))(-2 + x)(1 + x)
fx = (1 + -3i + -1x + -3i + 3ix + 9i2 + (3ix + -1x + x2))(-2 + x)(1 + x)

Reorder the terms:
fx = (1 + -3i + -3i + 3ix + 3ix + 9i2 + -1x + -1x + x2)(-2 + x)(1 + x)

Combine like terms: -3i + -3i = -6i
fx = (1 + -6i + 3ix + 3ix + 9i2 + -1x + -1x + x2)(-2 + x)(1 + x)

Combine like terms: 3ix + 3ix = 6ix
fx = (1 + -6i + 6ix + 9i2 + -1x + -1x + x2)(-2 + x)(1 + x)

Combine like terms: -1x + -1x = -2x
fx = (1 + -6i + 6ix + 9i2 + -2x + x2)(-2 + x)(1 + x)

Multiply (1 + -6i + 6ix + 9i2 + -2x + x2) * (-2 + x)
fx = (1(-2 + x) + -6i * (-2 + x) + 6ix * (-2 + x) + 9i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = ((-2 * 1 + x * 1) + -6i * (-2 + x) + 6ix * (-2 + x) + 9i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = ((-2 + 1x) + -6i * (-2 + x) + 6ix * (-2 + x) + 9i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + (-2 * -6i + x * -6i) + 6ix * (-2 + x) + 9i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + (12i + -6ix) + 6ix * (-2 + x) + 9i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + 12i + -6ix + (-2 * 6ix + x * 6ix) + 9i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + 12i + -6ix + (-12ix + 6ix2) + 9i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + 12i + -6ix + -12ix + 6ix2 + (-2 * 9i2 + x * 9i2) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + 12i + -6ix + -12ix + 6ix2 + (-18i2 + 9i2x) + -2x * (-2 + x) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + 12i + -6ix + -12ix + 6ix2 + -18i2 + 9i2x + (-2 * -2x + x * -2x) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + 12i + -6ix + -12ix + 6ix2 + -18i2 + 9i2x + (4x + -2x2) + x2(-2 + x))(1 + x)
fx = (-2 + 1x + 12i + -6ix + -12ix + 6ix2 + -18i2 + 9i2x + 4x + -2x2 + (-2 * x2 + x * x2))(1 + x)
fx = (-2 + 1x + 12i + -6ix + -12ix + 6ix2 + -18i2 + 9i2x + 4x + -2x2 + (-2x2 + x3))(1 + x)

Reorder the terms:
fx = (-2 + 12i + -6ix + -12ix + 6ix2 + -18i2 + 9i2x + 1x + 4x + -2x2 + -2x2 + x3)(1 + x)

Combine like terms: -6ix + -12ix = -18ix
fx = (-2 + 12i + -18ix + 6ix2 + -18i2 + 9i2x + 1x + 4x + -2x2 + -2x2 + x3)(1 + x)

Combine like terms: 1x + 4x = 5x
fx = (-2 + 12i + -18ix + 6ix2 + -18i2 + 9i2x + 5x + -2x2 + -2x2 + x3)(1 + x)

Combine like terms: -2x2 + -2x2 = -4x2
fx = (-2 + 12i + -18ix + 6ix2 + -18i2 + 9i2x + 5x + -4x2 + x3)(1 + x)

Multiply (-2 + 12i + -18ix + 6ix2 + -18i2 + 9i2x + 5x + -4x2 + x3) * (1 + x)
fx = (-2(1 + x) + 12i * (1 + x) + -18ix * (1 + x) + 6ix2 * (1 + x) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = ((1 * -2 + x * -2) + 12i * (1 + x) + -18ix * (1 + x) + 6ix2 * (1 + x) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = ((-2 + -2x) + 12i * (1 + x) + -18ix * (1 + x) + 6ix2 * (1 + x) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + (1 * 12i + x * 12i) + -18ix * (1 + x) + 6ix2 * (1 + x) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + (12i + 12ix) + -18ix * (1 + x) + 6ix2 * (1 + x) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + (1 * -18ix + x * -18ix) + 6ix2 * (1 + x) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + (-18ix + -18ix2) + 6ix2 * (1 + x) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + (1 * 6ix2 + x * 6ix2) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + (6ix2 + 6ix3) + -18i2 * (1 + x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + (1 * -18i2 + x * -18i2) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + (-18i2 + -18i2x) + 9i2x * (1 + x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + (1 * 9i2x + x * 9i2x) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + (9i2x + 9i2x2) + 5x * (1 + x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + (1 * 5x + x * 5x) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + (5x + 5x2) + -4x2 * (1 + x) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + 5x + 5x2 + (1 * -4x2 + x * -4x2) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + 5x + 5x2 + (-4x2 + -4x3) + x3(1 + x))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + 5x + 5x2 + -4x2 + -4x3 + (1 * x3 + x * x3))
fx = (-2 + -2x + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + 5x + 5x2 + -4x2 + -4x3 + (1x3 + x4))

Reorder the terms:
fx = (-2 + 12i + 12ix + -18ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + -2x + 5x + 5x2 + -4x2 + -4x3 + 1x3 + x4)

Combine like terms: 12ix + -18ix = -6ix
fx = (-2 + 12i + -6ix + -18ix2 + 6ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + -2x + 5x + 5x2 + -4x2 + -4x3 + 1x3 + x4)

Combine like terms: -18ix2 + 6ix2 = -12ix2
fx = (-2 + 12i + -6ix + -12ix2 + 6ix3 + -18i2 + -18i2x + 9i2x + 9i2x2 + -2x + 5x + 5x2 + -4x2 + -4x3 + 1x3 + x4)

Combine like terms: -18i2x + 9i2x = -9i2x
fx = (-2 + 12i + -6ix + -12ix2 + 6ix3 + -18i2 + -9i2x + 9i2x2 + -2x + 5x + 5x2 + -4x2 + -4x3 + 1x3 + x4)

Combine like terms: -2x + 5x = 3x
fx = (-2 + 12i + -6ix + -12ix2 + 6ix3 + -18i2 + -9i2x + 9i2x2 + 3x + 5x2 + -4x2 + -4x3 + 1x3 + x4)

Combine like terms: 5x2 + -4x2 = 1x2
fx = (-2 + 12i + -6ix + -12ix2 + 6ix3 + -18i2 + -9i2x + 9i2x2 + 3x + 1x2 + -4x3 + 1x3 + x4)

Combine like terms: -4x3 + 1x3 = -3x3
fx = (-2 + 12i + -6ix + -12ix2 + 6ix3 + -18i2 + -9i2x + 9i2x2 + 3x + 1x2 + -3x3 + x4)

Solving
fx = -2 + 12i + -6ix + -12ix2 + 6ix3 + -18i2 + -9i2x + 9i2x2 + 3x + 1x2 + -3x3 + x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -2x-1 + 12ix-1 + -6i + -12ix + 6ix2 + -18i2x-1 + -9i2 + 9i2x + 3 + x + -3x2 + x3

Simplifying
f = -2x-1 + 12ix-1 + -6i + -12ix + 6ix2 + -18i2x-1 + -9i2 + 9i2x + 3 + x + -3x2 + x3

Reorder the terms:
f = 3 + -6i + 12ix-1 + -12ix + 6ix2 + -9i2 + -18i2x-1 + 9i2x + -2x-1 + x + -3x2 + x3

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