f(x)=(x-4)(x-3-5i)(x-3+5i)

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Solution for f(x)=(x-4)(x-3-5i)(x-3+5i) equation: 


Simplifying
f(x) = (x + -4)(x + -3 + -5i)(x + -3 + 5i)

Multiply f * x
fx = (x + -4)(x + -3 + -5i)(x + -3 + 5i)

Reorder the terms:
fx = (-4 + x)(x + -3 + -5i)(x + -3 + 5i)

Reorder the terms:
fx = (-4 + x)(-3 + -5i + x)(x + -3 + 5i)

Reorder the terms:
fx = (-4 + x)(-3 + -5i + x)(-3 + 5i + x)

Multiply (-4 + x) * (-3 + -5i + x)
fx = (-4(-3 + -5i + x) + x(-3 + -5i + x))(-3 + 5i + x)
fx = ((-3 * -4 + -5i * -4 + x * -4) + x(-3 + -5i + x))(-3 + 5i + x)
fx = ((12 + 20i + -4x) + x(-3 + -5i + x))(-3 + 5i + x)
fx = (12 + 20i + -4x + (-3 * x + -5i * x + x * x))(-3 + 5i + x)

Reorder the terms:
fx = (12 + 20i + -4x + (-5ix + -3x + x2))(-3 + 5i + x)
fx = (12 + 20i + -4x + (-5ix + -3x + x2))(-3 + 5i + x)

Reorder the terms:
fx = (12 + 20i + -5ix + -4x + -3x + x2)(-3 + 5i + x)

Combine like terms: -4x + -3x = -7x
fx = (12 + 20i + -5ix + -7x + x2)(-3 + 5i + x)

Multiply (12 + 20i + -5ix + -7x + x2) * (-3 + 5i + x)
fx = (12(-3 + 5i + x) + 20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = ((-3 * 12 + 5i * 12 + x * 12) + 20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = ((-36 + 60i + 12x) + 20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (-36 + 60i + 12x + (-3 * 20i + 5i * 20i + x * 20i) + -5ix * (-3 + 5i + x) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))

Reorder the terms:
fx = (-36 + 60i + 12x + (-60i + 20ix + 100i2) + -5ix * (-3 + 5i + x) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (-36 + 60i + 12x + (-60i + 20ix + 100i2) + -5ix * (-3 + 5i + x) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + (-3 * -5ix + 5i * -5ix + x * -5ix) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))

Reorder the terms:
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + (15ix + -5ix2 + -25i2x) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + (15ix + -5ix2 + -25i2x) + -7x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + 15ix + -5ix2 + -25i2x + (-3 * -7x + 5i * -7x + x * -7x) + x2(-3 + 5i + x))

Reorder the terms:
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + 15ix + -5ix2 + -25i2x + (-35ix + 21x + -7x2) + x2(-3 + 5i + x))
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + 15ix + -5ix2 + -25i2x + (-35ix + 21x + -7x2) + x2(-3 + 5i + x))
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + 15ix + -5ix2 + -25i2x + -35ix + 21x + -7x2 + (-3 * x2 + 5i * x2 + x * x2))

Reorder the terms:
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + 15ix + -5ix2 + -25i2x + -35ix + 21x + -7x2 + (5ix2 + -3x2 + x3))
fx = (-36 + 60i + 12x + -60i + 20ix + 100i2 + 15ix + -5ix2 + -25i2x + -35ix + 21x + -7x2 + (5ix2 + -3x2 + x3))

Reorder the terms:
fx = (-36 + 60i + -60i + 20ix + 15ix + -35ix + -5ix2 + 5ix2 + 100i2 + -25i2x + 12x + 21x + -7x2 + -3x2 + x3)

Combine like terms: 60i + -60i = 0
fx = (-36 + 0 + 20ix + 15ix + -35ix + -5ix2 + 5ix2 + 100i2 + -25i2x + 12x + 21x + -7x2 + -3x2 + x3)
fx = (-36 + 20ix + 15ix + -35ix + -5ix2 + 5ix2 + 100i2 + -25i2x + 12x + 21x + -7x2 + -3x2 + x3)

Combine like terms: 20ix + 15ix = 35ix
fx = (-36 + 35ix + -35ix + -5ix2 + 5ix2 + 100i2 + -25i2x + 12x + 21x + -7x2 + -3x2 + x3)

Combine like terms: 35ix + -35ix = 0
fx = (-36 + 0 + -5ix2 + 5ix2 + 100i2 + -25i2x + 12x + 21x + -7x2 + -3x2 + x3)
fx = (-36 + -5ix2 + 5ix2 + 100i2 + -25i2x + 12x + 21x + -7x2 + -3x2 + x3)

Combine like terms: -5ix2 + 5ix2 = 0
fx = (-36 + 0 + 100i2 + -25i2x + 12x + 21x + -7x2 + -3x2 + x3)
fx = (-36 + 100i2 + -25i2x + 12x + 21x + -7x2 + -3x2 + x3)

Combine like terms: 12x + 21x = 33x
fx = (-36 + 100i2 + -25i2x + 33x + -7x2 + -3x2 + x3)

Combine like terms: -7x2 + -3x2 = -10x2
fx = (-36 + 100i2 + -25i2x + 33x + -10x2 + x3)

Solving
fx = -36 + 100i2 + -25i2x + 33x + -10x2 + 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 = -36x-1 + 100i2x-1 + -25i2 + 33 + -10x + x2

Simplifying
f = -36x-1 + 100i2x-1 + -25i2 + 33 + -10x + x2

Reorder the terms:
f = 33 + -25i2 + 100i2x-1 + -36x-1 + -10x + x2

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