f(x)=(x-4)(x-8i)(x+8i)

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Solution for f(x)=(x-4)(x-8i)(x+8i) equation: 


Simplifying
f(x) = (x + -4)(x + -8i)(x + 8i)

Multiply f * x
fx = (x + -4)(x + -8i)(x + 8i)

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

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

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

Multiply (-4 + x) * (-8i + x)
fx = (-4(-8i + x) + x(-8i + x))(8i + x)
fx = ((-8i * -4 + x * -4) + x(-8i + x))(8i + x)
fx = ((32i + -4x) + x(-8i + x))(8i + x)
fx = (32i + -4x + (-8i * x + x * x))(8i + x)
fx = (32i + -4x + (-8ix + x2))(8i + x)

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

Multiply (32i + -8ix + -4x + x2) * (8i + x)
fx = (32i * (8i + x) + -8ix * (8i + x) + -4x * (8i + x) + x2(8i + x))
fx = ((8i * 32i + x * 32i) + -8ix * (8i + x) + -4x * (8i + x) + x2(8i + x))

Reorder the terms:
fx = ((32ix + 256i2) + -8ix * (8i + x) + -4x * (8i + x) + x2(8i + x))
fx = ((32ix + 256i2) + -8ix * (8i + x) + -4x * (8i + x) + x2(8i + x))
fx = (32ix + 256i2 + (8i * -8ix + x * -8ix) + -4x * (8i + x) + x2(8i + x))

Reorder the terms:
fx = (32ix + 256i2 + (-8ix2 + -64i2x) + -4x * (8i + x) + x2(8i + x))
fx = (32ix + 256i2 + (-8ix2 + -64i2x) + -4x * (8i + x) + x2(8i + x))
fx = (32ix + 256i2 + -8ix2 + -64i2x + (8i * -4x + x * -4x) + x2(8i + x))
fx = (32ix + 256i2 + -8ix2 + -64i2x + (-32ix + -4x2) + x2(8i + x))
fx = (32ix + 256i2 + -8ix2 + -64i2x + -32ix + -4x2 + (8i * x2 + x * x2))
fx = (32ix + 256i2 + -8ix2 + -64i2x + -32ix + -4x2 + (8ix2 + x3))

Reorder the terms:
fx = (32ix + -32ix + -8ix2 + 8ix2 + 256i2 + -64i2x + -4x2 + x3)

Combine like terms: 32ix + -32ix = 0
fx = (0 + -8ix2 + 8ix2 + 256i2 + -64i2x + -4x2 + x3)
fx = (-8ix2 + 8ix2 + 256i2 + -64i2x + -4x2 + x3)

Combine like terms: -8ix2 + 8ix2 = 0
fx = (0 + 256i2 + -64i2x + -4x2 + x3)
fx = (256i2 + -64i2x + -4x2 + x3)

Solving
fx = 256i2 + -64i2x + -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 = 256i2x-1 + -64i2 + -4x + x2

Simplifying
f = 256i2x-1 + -64i2 + -4x + x2

Reorder the terms:
f = -64i2 + 256i2x-1 + -4x + x2

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