f(x)=(x+3)(x-8-4i)(x-8+4i)

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Solution for f(x)=(x+3)(x-8-4i)(x-8+4i) equation: 


Simplifying
f(x) = (x + 3)(x + -8 + -4i)(x + -8 + 4i)

Multiply f * x
fx = (x + 3)(x + -8 + -4i)(x + -8 + 4i)

Reorder the terms:
fx = (3 + x)(x + -8 + -4i)(x + -8 + 4i)

Reorder the terms:
fx = (3 + x)(-8 + -4i + x)(x + -8 + 4i)

Reorder the terms:
fx = (3 + x)(-8 + -4i + x)(-8 + 4i + x)

Multiply (3 + x) * (-8 + -4i + x)
fx = (3(-8 + -4i + x) + x(-8 + -4i + x))(-8 + 4i + x)
fx = ((-8 * 3 + -4i * 3 + x * 3) + x(-8 + -4i + x))(-8 + 4i + x)
fx = ((-24 + -12i + 3x) + x(-8 + -4i + x))(-8 + 4i + x)
fx = (-24 + -12i + 3x + (-8 * x + -4i * x + x * x))(-8 + 4i + x)

Reorder the terms:
fx = (-24 + -12i + 3x + (-4ix + -8x + x2))(-8 + 4i + x)
fx = (-24 + -12i + 3x + (-4ix + -8x + x2))(-8 + 4i + x)

Reorder the terms:
fx = (-24 + -12i + -4ix + 3x + -8x + x2)(-8 + 4i + x)

Combine like terms: 3x + -8x = -5x
fx = (-24 + -12i + -4ix + -5x + x2)(-8 + 4i + x)

Multiply (-24 + -12i + -4ix + -5x + x2) * (-8 + 4i + x)
fx = (-24(-8 + 4i + x) + -12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = ((-8 * -24 + 4i * -24 + x * -24) + -12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = ((192 + -96i + -24x) + -12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (192 + -96i + -24x + (-8 * -12i + 4i * -12i + x * -12i) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))

Reorder the terms:
fx = (192 + -96i + -24x + (96i + -12ix + -48i2) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (192 + -96i + -24x + (96i + -12ix + -48i2) + -4ix * (-8 + 4i + x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + (-8 * -4ix + 4i * -4ix + x * -4ix) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))

Reorder the terms:
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + (32ix + -4ix2 + -16i2x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + (32ix + -4ix2 + -16i2x) + -5x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + (-8 * -5x + 4i * -5x + x * -5x) + x2(-8 + 4i + x))

Reorder the terms:
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + (-20ix + 40x + -5x2) + x2(-8 + 4i + x))
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + (-20ix + 40x + -5x2) + x2(-8 + 4i + x))
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + -20ix + 40x + -5x2 + (-8 * x2 + 4i * x2 + x * x2))

Reorder the terms:
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + -20ix + 40x + -5x2 + (4ix2 + -8x2 + x3))
fx = (192 + -96i + -24x + 96i + -12ix + -48i2 + 32ix + -4ix2 + -16i2x + -20ix + 40x + -5x2 + (4ix2 + -8x2 + x3))

Reorder the terms:
fx = (192 + -96i + 96i + -12ix + 32ix + -20ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3)

Combine like terms: -96i + 96i = 0
fx = (192 + 0 + -12ix + 32ix + -20ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3)
fx = (192 + -12ix + 32ix + -20ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3)

Combine like terms: -12ix + 32ix = 20ix
fx = (192 + 20ix + -20ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3)

Combine like terms: 20ix + -20ix = 0
fx = (192 + 0 + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3)
fx = (192 + -4ix2 + 4ix2 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3)

Combine like terms: -4ix2 + 4ix2 = 0
fx = (192 + 0 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3)
fx = (192 + -48i2 + -16i2x + -24x + 40x + -5x2 + -8x2 + x3)

Combine like terms: -24x + 40x = 16x
fx = (192 + -48i2 + -16i2x + 16x + -5x2 + -8x2 + x3)

Combine like terms: -5x2 + -8x2 = -13x2
fx = (192 + -48i2 + -16i2x + 16x + -13x2 + x3)

Solving
fx = 192 + -48i2 + -16i2x + 16x + -13x2 + x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 192x-1 + -48i2x-1 + -16i2 + 16 + -13x + x2

Simplifying
f = 192x-1 + -48i2x-1 + -16i2 + 16 + -13x + x2

Reorder the terms:
f = 16 + -16i2 + -48i2x-1 + 192x-1 + -13x + x2

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