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

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


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

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

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

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

Multiply (-4 + -4i + x) * (-4 + 4i + x)
fx = (-4(-4 + 4i + x) + -4i * (-4 + 4i + x) + x(-4 + 4i + x))
fx = ((-4 * -4 + 4i * -4 + x * -4) + -4i * (-4 + 4i + x) + x(-4 + 4i + x))
fx = ((16 + -16i + -4x) + -4i * (-4 + 4i + x) + x(-4 + 4i + x))
fx = (16 + -16i + -4x + (-4 * -4i + 4i * -4i + x * -4i) + x(-4 + 4i + x))

Reorder the terms:
fx = (16 + -16i + -4x + (16i + -4ix + -16i2) + x(-4 + 4i + x))
fx = (16 + -16i + -4x + (16i + -4ix + -16i2) + x(-4 + 4i + x))
fx = (16 + -16i + -4x + 16i + -4ix + -16i2 + (-4 * x + 4i * x + x * x))

Reorder the terms:
fx = (16 + -16i + -4x + 16i + -4ix + -16i2 + (4ix + -4x + x2))
fx = (16 + -16i + -4x + 16i + -4ix + -16i2 + (4ix + -4x + x2))

Reorder the terms:
fx = (16 + -16i + 16i + -4ix + 4ix + -16i2 + -4x + -4x + x2)

Combine like terms: -16i + 16i = 0
fx = (16 + 0 + -4ix + 4ix + -16i2 + -4x + -4x + x2)
fx = (16 + -4ix + 4ix + -16i2 + -4x + -4x + x2)

Combine like terms: -4ix + 4ix = 0
fx = (16 + 0 + -16i2 + -4x + -4x + x2)
fx = (16 + -16i2 + -4x + -4x + x2)

Combine like terms: -4x + -4x = -8x
fx = (16 + -16i2 + -8x + x2)

Solving
fx = 16 + -16i2 + -8x + x2

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 16x-1 + -16i2x-1 + -8 + x

Simplifying
f = 16x-1 + -16i2x-1 + -8 + x

Reorder the terms:
f = -8 + -16i2x-1 + 16x-1 + x

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