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 = -11x
fx = (24 + 12i + -4ix + -11x + x2)(-8 + 4i + x)

Multiply (24 + 12i + -4ix + -11x + x2) * (-8 + 4i + x)
fx = (24(-8 + 4i + x) + 12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = ((-8 * 24 + 4i * 24 + x * 24) + 12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = ((-192 + 96i + 24x) + 12i * (-8 + 4i + x) + -4ix * (-8 + 4i + x) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (-192 + 96i + 24x + (-8 * 12i + 4i * 12i + x * 12i) + -4ix * (-8 + 4i + x) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))

Reorder the terms:
fx = (-192 + 96i + 24x + (-96i + 12ix + 48i2) + -4ix * (-8 + 4i + x) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (-192 + 96i + 24x + (-96i + 12ix + 48i2) + -4ix * (-8 + 4i + x) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + (-8 * -4ix + 4i * -4ix + x * -4ix) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))

Reorder the terms:
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + (32ix + -4ix2 + -16i2x) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + (32ix + -4ix2 + -16i2x) + -11x * (-8 + 4i + x) + x2(-8 + 4i + x))
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + 32ix + -4ix2 + -16i2x + (-8 * -11x + 4i * -11x + x * -11x) + x2(-8 + 4i + x))

Reorder the terms:
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + 32ix + -4ix2 + -16i2x + (-44ix + 88x + -11x2) + x2(-8 + 4i + x))
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + 32ix + -4ix2 + -16i2x + (-44ix + 88x + -11x2) + x2(-8 + 4i + x))
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + 32ix + -4ix2 + -16i2x + -44ix + 88x + -11x2 + (-8 * x2 + 4i * x2 + x * x2))

Reorder the terms:
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + 32ix + -4ix2 + -16i2x + -44ix + 88x + -11x2 + (4ix2 + -8x2 + x3))
fx = (-192 + 96i + 24x + -96i + 12ix + 48i2 + 32ix + -4ix2 + -16i2x + -44ix + 88x + -11x2 + (4ix2 + -8x2 + x3))

Reorder the terms:
fx = (-192 + 96i + -96i + 12ix + 32ix + -44ix + -4ix2 + 4ix2 + 48i2 + -16i2x + 24x + 88x + -11x2 + -8x2 + x3)

Combine like terms: 96i + -96i = 0
fx = (-192 + 0 + 12ix + 32ix + -44ix + -4ix2 + 4ix2 + 48i2 + -16i2x + 24x + 88x + -11x2 + -8x2 + x3)
fx = (-192 + 12ix + 32ix + -44ix + -4ix2 + 4ix2 + 48i2 + -16i2x + 24x + 88x + -11x2 + -8x2 + x3)

Combine like terms: 12ix + 32ix = 44ix
fx = (-192 + 44ix + -44ix + -4ix2 + 4ix2 + 48i2 + -16i2x + 24x + 88x + -11x2 + -8x2 + x3)

Combine like terms: 44ix + -44ix = 0
fx = (-192 + 0 + -4ix2 + 4ix2 + 48i2 + -16i2x + 24x + 88x + -11x2 + -8x2 + x3)
fx = (-192 + -4ix2 + 4ix2 + 48i2 + -16i2x + 24x + 88x + -11x2 + -8x2 + x3)

Combine like terms: -4ix2 + 4ix2 = 0
fx = (-192 + 0 + 48i2 + -16i2x + 24x + 88x + -11x2 + -8x2 + x3)
fx = (-192 + 48i2 + -16i2x + 24x + 88x + -11x2 + -8x2 + x3)

Combine like terms: 24x + 88x = 112x
fx = (-192 + 48i2 + -16i2x + 112x + -11x2 + -8x2 + x3)

Combine like terms: -11x2 + -8x2 = -19x2
fx = (-192 + 48i2 + -16i2x + 112x + -19x2 + x3)

Solving
fx = -192 + 48i2 + -16i2x + 112x + -19x2 + 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 + 112 + -19x + x2

Simplifying
f = -192x-1 + 48i2x-1 + -16i2 + 112 + -19x + x2

Reorder the terms:
f = 112 + -16i2 + 48i2x-1 + -192x-1 + -19x + x2

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