f(x)=(x+2)(x-4)(x-1-3i)(x-1+3i)

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Solution for f(x)=(x+2)(x-4)(x-1-3i)(x-1+3i) equation: 


Simplifying
f(x) = (x + 2)(x + -4)(x + -1 + -3i)(x + -1 + 3i)

Multiply f * x
fx = (x + 2)(x + -4)(x + -1 + -3i)(x + -1 + 3i)

Reorder the terms:
fx = (2 + x)(x + -4)(x + -1 + -3i)(x + -1 + 3i)

Reorder the terms:
fx = (2 + x)(-4 + x)(x + -1 + -3i)(x + -1 + 3i)

Reorder the terms:
fx = (2 + x)(-4 + x)(-1 + -3i + x)(x + -1 + 3i)

Reorder the terms:
fx = (2 + x)(-4 + x)(-1 + -3i + x)(-1 + 3i + x)

Multiply (2 + x) * (-4 + x)
fx = (2(-4 + x) + x(-4 + x))(-1 + -3i + x)(-1 + 3i + x)
fx = ((-4 * 2 + x * 2) + x(-4 + x))(-1 + -3i + x)(-1 + 3i + x)
fx = ((-8 + 2x) + x(-4 + x))(-1 + -3i + x)(-1 + 3i + x)
fx = (-8 + 2x + (-4 * x + x * x))(-1 + -3i + x)(-1 + 3i + x)
fx = (-8 + 2x + (-4x + x2))(-1 + -3i + x)(-1 + 3i + x)

Combine like terms: 2x + -4x = -2x
fx = (-8 + -2x + x2)(-1 + -3i + x)(-1 + 3i + x)

Multiply (-8 + -2x + x2) * (-1 + -3i + x)
fx = (-8(-1 + -3i + x) + -2x * (-1 + -3i + x) + x2(-1 + -3i + x))(-1 + 3i + x)
fx = ((-1 * -8 + -3i * -8 + x * -8) + -2x * (-1 + -3i + x) + x2(-1 + -3i + x))(-1 + 3i + x)
fx = ((8 + 24i + -8x) + -2x * (-1 + -3i + x) + x2(-1 + -3i + x))(-1 + 3i + x)
fx = (8 + 24i + -8x + (-1 * -2x + -3i * -2x + x * -2x) + x2(-1 + -3i + x))(-1 + 3i + x)

Reorder the terms:
fx = (8 + 24i + -8x + (6ix + 2x + -2x2) + x2(-1 + -3i + x))(-1 + 3i + x)
fx = (8 + 24i + -8x + (6ix + 2x + -2x2) + x2(-1 + -3i + x))(-1 + 3i + x)
fx = (8 + 24i + -8x + 6ix + 2x + -2x2 + (-1 * x2 + -3i * x2 + x * x2))(-1 + 3i + x)

Reorder the terms:
fx = (8 + 24i + -8x + 6ix + 2x + -2x2 + (-3ix2 + -1x2 + x3))(-1 + 3i + x)
fx = (8 + 24i + -8x + 6ix + 2x + -2x2 + (-3ix2 + -1x2 + x3))(-1 + 3i + x)

Reorder the terms:
fx = (8 + 24i + 6ix + -3ix2 + -8x + 2x + -2x2 + -1x2 + x3)(-1 + 3i + x)

Combine like terms: -8x + 2x = -6x
fx = (8 + 24i + 6ix + -3ix2 + -6x + -2x2 + -1x2 + x3)(-1 + 3i + x)

Combine like terms: -2x2 + -1x2 = -3x2
fx = (8 + 24i + 6ix + -3ix2 + -6x + -3x2 + x3)(-1 + 3i + x)

Multiply (8 + 24i + 6ix + -3ix2 + -6x + -3x2 + x3) * (-1 + 3i + x)
fx = (8(-1 + 3i + x) + 24i * (-1 + 3i + x) + 6ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = ((-1 * 8 + 3i * 8 + x * 8) + 24i * (-1 + 3i + x) + 6ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = ((-8 + 24i + 8x) + 24i * (-1 + 3i + x) + 6ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + (-1 * 24i + 3i * 24i + x * 24i) + 6ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))

Reorder the terms:
fx = (-8 + 24i + 8x + (-24i + 24ix + 72i2) + 6ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + (-24i + 24ix + 72i2) + 6ix * (-1 + 3i + x) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + (-1 * 6ix + 3i * 6ix + x * 6ix) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))

Reorder the terms:
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + (-6ix + 6ix2 + 18i2x) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + (-6ix + 6ix2 + 18i2x) + -3ix2 * (-1 + 3i + x) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + (-1 * -3ix2 + 3i * -3ix2 + x * -3ix2) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))

Reorder the terms:
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + (3ix2 + -3ix3 + -9i2x2) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + (3ix2 + -3ix3 + -9i2x2) + -6x * (-1 + 3i + x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + (-1 * -6x + 3i * -6x + x * -6x) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))

Reorder the terms:
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + (-18ix + 6x + -6x2) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + (-18ix + 6x + -6x2) + -3x2 * (-1 + 3i + x) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + -18ix + 6x + -6x2 + (-1 * -3x2 + 3i * -3x2 + x * -3x2) + x3(-1 + 3i + x))

Reorder the terms:
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + -18ix + 6x + -6x2 + (-9ix2 + 3x2 + -3x3) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + -18ix + 6x + -6x2 + (-9ix2 + 3x2 + -3x3) + x3(-1 + 3i + x))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + -18ix + 6x + -6x2 + -9ix2 + 3x2 + -3x3 + (-1 * x3 + 3i * x3 + x * x3))

Reorder the terms:
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + -18ix + 6x + -6x2 + -9ix2 + 3x2 + -3x3 + (3ix3 + -1x3 + x4))
fx = (-8 + 24i + 8x + -24i + 24ix + 72i2 + -6ix + 6ix2 + 18i2x + 3ix2 + -3ix3 + -9i2x2 + -18ix + 6x + -6x2 + -9ix2 + 3x2 + -3x3 + (3ix3 + -1x3 + x4))

Reorder the terms:
fx = (-8 + 24i + -24i + 24ix + -6ix + -18ix + 6ix2 + 3ix2 + -9ix2 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)

Combine like terms: 24i + -24i = 0
fx = (-8 + 0 + 24ix + -6ix + -18ix + 6ix2 + 3ix2 + -9ix2 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)
fx = (-8 + 24ix + -6ix + -18ix + 6ix2 + 3ix2 + -9ix2 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)

Combine like terms: 24ix + -6ix = 18ix
fx = (-8 + 18ix + -18ix + 6ix2 + 3ix2 + -9ix2 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)

Combine like terms: 18ix + -18ix = 0
fx = (-8 + 0 + 6ix2 + 3ix2 + -9ix2 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)
fx = (-8 + 6ix2 + 3ix2 + -9ix2 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)

Combine like terms: 6ix2 + 3ix2 = 9ix2
fx = (-8 + 9ix2 + -9ix2 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)

Combine like terms: 9ix2 + -9ix2 = 0
fx = (-8 + 0 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)
fx = (-8 + -3ix3 + 3ix3 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)

Combine like terms: -3ix3 + 3ix3 = 0
fx = (-8 + 0 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)
fx = (-8 + 72i2 + 18i2x + -9i2x2 + 8x + 6x + -6x2 + 3x2 + -3x3 + -1x3 + x4)

Combine like terms: 8x + 6x = 14x
fx = (-8 + 72i2 + 18i2x + -9i2x2 + 14x + -6x2 + 3x2 + -3x3 + -1x3 + x4)

Combine like terms: -6x2 + 3x2 = -3x2
fx = (-8 + 72i2 + 18i2x + -9i2x2 + 14x + -3x2 + -3x3 + -1x3 + x4)

Combine like terms: -3x3 + -1x3 = -4x3
fx = (-8 + 72i2 + 18i2x + -9i2x2 + 14x + -3x2 + -4x3 + x4)

Solving
fx = -8 + 72i2 + 18i2x + -9i2x2 + 14x + -3x2 + -4x3 + 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 = -8x-1 + 72i2x-1 + 18i2 + -9i2x + 14 + -3x + -4x2 + x3

Simplifying
f = -8x-1 + 72i2x-1 + 18i2 + -9i2x + 14 + -3x + -4x2 + x3

Reorder the terms:
f = 14 + 18i2 + 72i2x-1 + -9i2x + -8x-1 + -3x + -4x2 + x3

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