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

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


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

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

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

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

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

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

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

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

Combine like terms: 3x + -4x = -1x
fx = (-12 + -12i + -4ix + -1x + x2)(-4 + 4i + x)

Multiply (-12 + -12i + -4ix + -1x + x2) * (-4 + 4i + x)
fx = (-12(-4 + 4i + x) + -12i * (-4 + 4i + x) + -4ix * (-4 + 4i + x) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = ((-4 * -12 + 4i * -12 + x * -12) + -12i * (-4 + 4i + x) + -4ix * (-4 + 4i + x) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = ((48 + -48i + -12x) + -12i * (-4 + 4i + x) + -4ix * (-4 + 4i + x) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = (48 + -48i + -12x + (-4 * -12i + 4i * -12i + x * -12i) + -4ix * (-4 + 4i + x) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))

Reorder the terms:
fx = (48 + -48i + -12x + (48i + -12ix + -48i2) + -4ix * (-4 + 4i + x) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = (48 + -48i + -12x + (48i + -12ix + -48i2) + -4ix * (-4 + 4i + x) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + (-4 * -4ix + 4i * -4ix + x * -4ix) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))

Reorder the terms:
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + (16ix + -4ix2 + -16i2x) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + (16ix + -4ix2 + -16i2x) + -1x * (-4 + 4i + x) + x2(-4 + 4i + x))
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + 16ix + -4ix2 + -16i2x + (-4 * -1x + 4i * -1x + x * -1x) + x2(-4 + 4i + x))

Reorder the terms:
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + 16ix + -4ix2 + -16i2x + (-4ix + 4x + -1x2) + x2(-4 + 4i + x))
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + 16ix + -4ix2 + -16i2x + (-4ix + 4x + -1x2) + x2(-4 + 4i + x))
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + 16ix + -4ix2 + -16i2x + -4ix + 4x + -1x2 + (-4 * x2 + 4i * x2 + x * x2))

Reorder the terms:
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + 16ix + -4ix2 + -16i2x + -4ix + 4x + -1x2 + (4ix2 + -4x2 + x3))
fx = (48 + -48i + -12x + 48i + -12ix + -48i2 + 16ix + -4ix2 + -16i2x + -4ix + 4x + -1x2 + (4ix2 + -4x2 + x3))

Reorder the terms:
fx = (48 + -48i + 48i + -12ix + 16ix + -4ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -12x + 4x + -1x2 + -4x2 + x3)

Combine like terms: -48i + 48i = 0
fx = (48 + 0 + -12ix + 16ix + -4ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -12x + 4x + -1x2 + -4x2 + x3)
fx = (48 + -12ix + 16ix + -4ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -12x + 4x + -1x2 + -4x2 + x3)

Combine like terms: -12ix + 16ix = 4ix
fx = (48 + 4ix + -4ix + -4ix2 + 4ix2 + -48i2 + -16i2x + -12x + 4x + -1x2 + -4x2 + x3)

Combine like terms: 4ix + -4ix = 0
fx = (48 + 0 + -4ix2 + 4ix2 + -48i2 + -16i2x + -12x + 4x + -1x2 + -4x2 + x3)
fx = (48 + -4ix2 + 4ix2 + -48i2 + -16i2x + -12x + 4x + -1x2 + -4x2 + x3)

Combine like terms: -4ix2 + 4ix2 = 0
fx = (48 + 0 + -48i2 + -16i2x + -12x + 4x + -1x2 + -4x2 + x3)
fx = (48 + -48i2 + -16i2x + -12x + 4x + -1x2 + -4x2 + x3)

Combine like terms: -12x + 4x = -8x
fx = (48 + -48i2 + -16i2x + -8x + -1x2 + -4x2 + x3)

Combine like terms: -1x2 + -4x2 = -5x2
fx = (48 + -48i2 + -16i2x + -8x + -5x2 + x3)

Solving
fx = 48 + -48i2 + -16i2x + -8x + -5x2 + 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 = 48x-1 + -48i2x-1 + -16i2 + -8 + -5x + x2

Simplifying
f = 48x-1 + -48i2x-1 + -16i2 + -8 + -5x + x2

Reorder the terms:
f = -8 + -16i2 + -48i2x-1 + 48x-1 + -5x + x2

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