f(x)=(x+1)((x-4)-5i)((x-4)+5i)

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Solution for f(x)=(x+1)((x-4)-5i)((x-4)+5i) equation: 


Simplifying
f(x) = (x + 1)((x + -4) + -5i)((x + -4) + 5i)

Multiply f * x
fx = (x + 1)((x + -4) + -5i)((x + -4) + 5i)

Reorder the terms:
fx = (1 + x)((x + -4) + -5i)((x + -4) + 5i)

Reorder the terms:
fx = (1 + x)((-4 + x) + -5i)((x + -4) + 5i)

Remove parenthesis around (-4 + x)
fx = (1 + x)(-4 + x + -5i)((x + -4) + 5i)

Reorder the terms:
fx = (1 + x)(-4 + -5i + x)((x + -4) + 5i)

Reorder the terms:
fx = (1 + x)(-4 + -5i + x)((-4 + x) + 5i)

Remove parenthesis around (-4 + x)
fx = (1 + x)(-4 + -5i + x)(-4 + x + 5i)

Reorder the terms:
fx = (1 + x)(-4 + -5i + x)(-4 + 5i + x)

Multiply (1 + x) * (-4 + -5i + x)
fx = (1(-4 + -5i + x) + x(-4 + -5i + x))(-4 + 5i + x)
fx = ((-4 * 1 + -5i * 1 + x * 1) + x(-4 + -5i + x))(-4 + 5i + x)
fx = ((-4 + -5i + 1x) + x(-4 + -5i + x))(-4 + 5i + x)
fx = (-4 + -5i + 1x + (-4 * x + -5i * x + x * x))(-4 + 5i + x)

Reorder the terms:
fx = (-4 + -5i + 1x + (-5ix + -4x + x2))(-4 + 5i + x)
fx = (-4 + -5i + 1x + (-5ix + -4x + x2))(-4 + 5i + x)

Reorder the terms:
fx = (-4 + -5i + -5ix + 1x + -4x + x2)(-4 + 5i + x)

Combine like terms: 1x + -4x = -3x
fx = (-4 + -5i + -5ix + -3x + x2)(-4 + 5i + x)

Multiply (-4 + -5i + -5ix + -3x + x2) * (-4 + 5i + x)
fx = (-4(-4 + 5i + x) + -5i * (-4 + 5i + x) + -5ix * (-4 + 5i + x) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))
fx = ((-4 * -4 + 5i * -4 + x * -4) + -5i * (-4 + 5i + x) + -5ix * (-4 + 5i + x) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))
fx = ((16 + -20i + -4x) + -5i * (-4 + 5i + x) + -5ix * (-4 + 5i + x) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))
fx = (16 + -20i + -4x + (-4 * -5i + 5i * -5i + x * -5i) + -5ix * (-4 + 5i + x) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))

Reorder the terms:
fx = (16 + -20i + -4x + (20i + -5ix + -25i2) + -5ix * (-4 + 5i + x) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))
fx = (16 + -20i + -4x + (20i + -5ix + -25i2) + -5ix * (-4 + 5i + x) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + (-4 * -5ix + 5i * -5ix + x * -5ix) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))

Reorder the terms:
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + (20ix + -5ix2 + -25i2x) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + (20ix + -5ix2 + -25i2x) + -3x * (-4 + 5i + x) + x2(-4 + 5i + x))
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + 20ix + -5ix2 + -25i2x + (-4 * -3x + 5i * -3x + x * -3x) + x2(-4 + 5i + x))

Reorder the terms:
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + 20ix + -5ix2 + -25i2x + (-15ix + 12x + -3x2) + x2(-4 + 5i + x))
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + 20ix + -5ix2 + -25i2x + (-15ix + 12x + -3x2) + x2(-4 + 5i + x))
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + 20ix + -5ix2 + -25i2x + -15ix + 12x + -3x2 + (-4 * x2 + 5i * x2 + x * x2))

Reorder the terms:
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + 20ix + -5ix2 + -25i2x + -15ix + 12x + -3x2 + (5ix2 + -4x2 + x3))
fx = (16 + -20i + -4x + 20i + -5ix + -25i2 + 20ix + -5ix2 + -25i2x + -15ix + 12x + -3x2 + (5ix2 + -4x2 + x3))

Reorder the terms:
fx = (16 + -20i + 20i + -5ix + 20ix + -15ix + -5ix2 + 5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3)

Combine like terms: -20i + 20i = 0
fx = (16 + 0 + -5ix + 20ix + -15ix + -5ix2 + 5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3)
fx = (16 + -5ix + 20ix + -15ix + -5ix2 + 5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3)

Combine like terms: -5ix + 20ix = 15ix
fx = (16 + 15ix + -15ix + -5ix2 + 5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3)

Combine like terms: 15ix + -15ix = 0
fx = (16 + 0 + -5ix2 + 5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3)
fx = (16 + -5ix2 + 5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3)

Combine like terms: -5ix2 + 5ix2 = 0
fx = (16 + 0 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3)
fx = (16 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3)

Combine like terms: -4x + 12x = 8x
fx = (16 + -25i2 + -25i2x + 8x + -3x2 + -4x2 + x3)

Combine like terms: -3x2 + -4x2 = -7x2
fx = (16 + -25i2 + -25i2x + 8x + -7x2 + x3)

Solving
fx = 16 + -25i2 + -25i2x + 8x + -7x2 + 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 = 16x-1 + -25i2x-1 + -25i2 + 8 + -7x + x2

Simplifying
f = 16x-1 + -25i2x-1 + -25i2 + 8 + -7x + x2

Reorder the terms:
f = 8 + -25i2 + -25i2x-1 + 16x-1 + -7x + x2

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