f(x)=(x-5)(x-4i)(x+4i)

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Solution for f(x)=(x-5)(x-4i)(x+4i) equation:


Simplifying
f(x) = (x + -5)(x + -4i)(x + 4i)

Multiply f * x
fx = (x + -5)(x + -4i)(x + 4i)

Reorder the terms:
fx = (-5 + x)(x + -4i)(x + 4i)

Reorder the terms:
fx = (-5 + x)(-4i + x)(x + 4i)

Reorder the terms:
fx = (-5 + x)(-4i + x)(4i + x)

Multiply (-5 + x) * (-4i + x)
fx = (-5(-4i + x) + x(-4i + x))(4i + x)
fx = ((-4i * -5 + x * -5) + x(-4i + x))(4i + x)
fx = ((20i + -5x) + x(-4i + x))(4i + x)
fx = (20i + -5x + (-4i * x + x * x))(4i + x)
fx = (20i + -5x + (-4ix + x2))(4i + x)

Reorder the terms:
fx = (20i + -4ix + -5x + x2)(4i + x)
fx = (20i + -4ix + -5x + x2)(4i + x)

Multiply (20i + -4ix + -5x + x2) * (4i + x)
fx = (20i * (4i + x) + -4ix * (4i + x) + -5x * (4i + x) + x2(4i + x))
fx = ((4i * 20i + x * 20i) + -4ix * (4i + x) + -5x * (4i + x) + x2(4i + x))

Reorder the terms:
fx = ((20ix + 80i2) + -4ix * (4i + x) + -5x * (4i + x) + x2(4i + x))
fx = ((20ix + 80i2) + -4ix * (4i + x) + -5x * (4i + x) + x2(4i + x))
fx = (20ix + 80i2 + (4i * -4ix + x * -4ix) + -5x * (4i + x) + x2(4i + x))

Reorder the terms:
fx = (20ix + 80i2 + (-4ix2 + -16i2x) + -5x * (4i + x) + x2(4i + x))
fx = (20ix + 80i2 + (-4ix2 + -16i2x) + -5x * (4i + x) + x2(4i + x))
fx = (20ix + 80i2 + -4ix2 + -16i2x + (4i * -5x + x * -5x) + x2(4i + x))
fx = (20ix + 80i2 + -4ix2 + -16i2x + (-20ix + -5x2) + x2(4i + x))
fx = (20ix + 80i2 + -4ix2 + -16i2x + -20ix + -5x2 + (4i * x2 + x * x2))
fx = (20ix + 80i2 + -4ix2 + -16i2x + -20ix + -5x2 + (4ix2 + x3))

Reorder the terms:
fx = (20ix + -20ix + -4ix2 + 4ix2 + 80i2 + -16i2x + -5x2 + x3)

Combine like terms: 20ix + -20ix = 0
fx = (0 + -4ix2 + 4ix2 + 80i2 + -16i2x + -5x2 + x3)
fx = (-4ix2 + 4ix2 + 80i2 + -16i2x + -5x2 + x3)

Combine like terms: -4ix2 + 4ix2 = 0
fx = (0 + 80i2 + -16i2x + -5x2 + x3)
fx = (80i2 + -16i2x + -5x2 + x3)

Solving
fx = 80i2 + -16i2x + -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 = 80i2x-1 + -16i2 + -5x + x2

Simplifying
f = 80i2x-1 + -16i2 + -5x + x2

Reorder the terms:
f = -16i2 + 80i2x-1 + -5x + x2

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