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

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


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

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

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

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

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

Multiply (-4 + x) * (-4i + x)
fx = (-4(-4i + x) + x(-4i + x))(4i + x)
fx = ((-4i * -4 + x * -4) + x(-4i + x))(4i + x)
fx = ((16i + -4x) + x(-4i + x))(4i + x)
fx = (16i + -4x + (-4i * x + x * x))(4i + x)
fx = (16i + -4x + (-4ix + x2))(4i + x)

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

Multiply (16i + -4ix + -4x + x2) * (4i + x)
fx = (16i * (4i + x) + -4ix * (4i + x) + -4x * (4i + x) + x2(4i + x))
fx = ((4i * 16i + x * 16i) + -4ix * (4i + x) + -4x * (4i + x) + x2(4i + x))

Reorder the terms:
fx = ((16ix + 64i2) + -4ix * (4i + x) + -4x * (4i + x) + x2(4i + x))
fx = ((16ix + 64i2) + -4ix * (4i + x) + -4x * (4i + x) + x2(4i + x))
fx = (16ix + 64i2 + (4i * -4ix + x * -4ix) + -4x * (4i + x) + x2(4i + x))

Reorder the terms:
fx = (16ix + 64i2 + (-4ix2 + -16i2x) + -4x * (4i + x) + x2(4i + x))
fx = (16ix + 64i2 + (-4ix2 + -16i2x) + -4x * (4i + x) + x2(4i + x))
fx = (16ix + 64i2 + -4ix2 + -16i2x + (4i * -4x + x * -4x) + x2(4i + x))
fx = (16ix + 64i2 + -4ix2 + -16i2x + (-16ix + -4x2) + x2(4i + x))
fx = (16ix + 64i2 + -4ix2 + -16i2x + -16ix + -4x2 + (4i * x2 + x * x2))
fx = (16ix + 64i2 + -4ix2 + -16i2x + -16ix + -4x2 + (4ix2 + x3))

Reorder the terms:
fx = (16ix + -16ix + -4ix2 + 4ix2 + 64i2 + -16i2x + -4x2 + x3)

Combine like terms: 16ix + -16ix = 0
fx = (0 + -4ix2 + 4ix2 + 64i2 + -16i2x + -4x2 + x3)
fx = (-4ix2 + 4ix2 + 64i2 + -16i2x + -4x2 + x3)

Combine like terms: -4ix2 + 4ix2 = 0
fx = (0 + 64i2 + -16i2x + -4x2 + x3)
fx = (64i2 + -16i2x + -4x2 + x3)

Solving
fx = 64i2 + -16i2x + -4x2 + 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 = 64i2x-1 + -16i2 + -4x + x2

Simplifying
f = 64i2x-1 + -16i2 + -4x + x2

Reorder the terms:
f = -16i2 + 64i2x-1 + -4x + x2

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