f(x)=(x+2)(x-4i)(x+4i)

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Solution for f(x)=(x+2)(x-4i)(x+4i) equation: 


Simplifying
f(x) = (x + 2)(x + -4i)(x + 4i)

Multiply f * x
fx = (x + 2)(x + -4i)(x + 4i)

Reorder the terms:
fx = (2 + x)(x + -4i)(x + 4i)

Reorder the terms:
fx = (2 + x)(-4i + x)(x + 4i)

Reorder the terms:
fx = (2 + x)(-4i + x)(4i + x)

Multiply (2 + x) * (-4i + x)
fx = (2(-4i + x) + x(-4i + x))(4i + x)
fx = ((-4i * 2 + x * 2) + x(-4i + x))(4i + x)
fx = ((-8i + 2x) + x(-4i + x))(4i + x)
fx = (-8i + 2x + (-4i * x + x * x))(4i + x)
fx = (-8i + 2x + (-4ix + x2))(4i + x)

Reorder the terms:
fx = (-8i + -4ix + 2x + x2)(4i + x)
fx = (-8i + -4ix + 2x + x2)(4i + x)

Multiply (-8i + -4ix + 2x + x2) * (4i + x)
fx = (-8i * (4i + x) + -4ix * (4i + x) + 2x * (4i + x) + x2(4i + x))
fx = ((4i * -8i + x * -8i) + -4ix * (4i + x) + 2x * (4i + x) + x2(4i + x))

Reorder the terms:
fx = ((-8ix + -32i2) + -4ix * (4i + x) + 2x * (4i + x) + x2(4i + x))
fx = ((-8ix + -32i2) + -4ix * (4i + x) + 2x * (4i + x) + x2(4i + x))
fx = (-8ix + -32i2 + (4i * -4ix + x * -4ix) + 2x * (4i + x) + x2(4i + x))

Reorder the terms:
fx = (-8ix + -32i2 + (-4ix2 + -16i2x) + 2x * (4i + x) + x2(4i + x))
fx = (-8ix + -32i2 + (-4ix2 + -16i2x) + 2x * (4i + x) + x2(4i + x))
fx = (-8ix + -32i2 + -4ix2 + -16i2x + (4i * 2x + x * 2x) + x2(4i + x))
fx = (-8ix + -32i2 + -4ix2 + -16i2x + (8ix + 2x2) + x2(4i + x))
fx = (-8ix + -32i2 + -4ix2 + -16i2x + 8ix + 2x2 + (4i * x2 + x * x2))
fx = (-8ix + -32i2 + -4ix2 + -16i2x + 8ix + 2x2 + (4ix2 + x3))

Reorder the terms:
fx = (-8ix + 8ix + -4ix2 + 4ix2 + -32i2 + -16i2x + 2x2 + x3)

Combine like terms: -8ix + 8ix = 0
fx = (0 + -4ix2 + 4ix2 + -32i2 + -16i2x + 2x2 + x3)
fx = (-4ix2 + 4ix2 + -32i2 + -16i2x + 2x2 + x3)

Combine like terms: -4ix2 + 4ix2 = 0
fx = (0 + -32i2 + -16i2x + 2x2 + x3)
fx = (-32i2 + -16i2x + 2x2 + x3)

Solving
fx = -32i2 + -16i2x + 2x2 + 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 = -32i2x-1 + -16i2 + 2x + x2

Simplifying
f = -32i2x-1 + -16i2 + 2x + x2

Reorder the terms:
f = -16i2 + -32i2x-1 + 2x + x2

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