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 = 1x
fx = (-12 + -20i + -5ix + 1x + x2)(-3 + 5i + x)

Multiply (-12 + -20i + -5ix + 1x + x2) * (-3 + 5i + x)
fx = (-12(-3 + 5i + x) + -20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = ((-3 * -12 + 5i * -12 + x * -12) + -20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = ((36 + -60i + -12x) + -20i * (-3 + 5i + x) + -5ix * (-3 + 5i + x) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (36 + -60i + -12x + (-3 * -20i + 5i * -20i + x * -20i) + -5ix * (-3 + 5i + x) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))

Reorder the terms:
fx = (36 + -60i + -12x + (60i + -20ix + -100i2) + -5ix * (-3 + 5i + x) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (36 + -60i + -12x + (60i + -20ix + -100i2) + -5ix * (-3 + 5i + x) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + (-3 * -5ix + 5i * -5ix + x * -5ix) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))

Reorder the terms:
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + (15ix + -5ix2 + -25i2x) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + (15ix + -5ix2 + -25i2x) + 1x * (-3 + 5i + x) + x2(-3 + 5i + x))
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + (-3 * 1x + 5i * 1x + x * 1x) + x2(-3 + 5i + x))

Reorder the terms:
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + (5ix + -3x + 1x2) + x2(-3 + 5i + x))
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + (5ix + -3x + 1x2) + x2(-3 + 5i + x))
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + 5ix + -3x + 1x2 + (-3 * x2 + 5i * x2 + x * x2))

Reorder the terms:
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + 5ix + -3x + 1x2 + (5ix2 + -3x2 + x3))
fx = (36 + -60i + -12x + 60i + -20ix + -100i2 + 15ix + -5ix2 + -25i2x + 5ix + -3x + 1x2 + (5ix2 + -3x2 + x3))

Reorder the terms:
fx = (36 + -60i + 60i + -20ix + 15ix + 5ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3)

Combine like terms: -60i + 60i = 0
fx = (36 + 0 + -20ix + 15ix + 5ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3)
fx = (36 + -20ix + 15ix + 5ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3)

Combine like terms: -20ix + 15ix = -5ix
fx = (36 + -5ix + 5ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3)

Combine like terms: -5ix + 5ix = 0
fx = (36 + 0 + -5ix2 + 5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3)
fx = (36 + -5ix2 + 5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3)

Combine like terms: -5ix2 + 5ix2 = 0
fx = (36 + 0 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3)
fx = (36 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3)

Combine like terms: -12x + -3x = -15x
fx = (36 + -100i2 + -25i2x + -15x + 1x2 + -3x2 + x3)

Combine like terms: 1x2 + -3x2 = -2x2
fx = (36 + -100i2 + -25i2x + -15x + -2x2 + x3)

Solving
fx = 36 + -100i2 + -25i2x + -15x + -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 = 36x-1 + -100i2x-1 + -25i2 + -15 + -2x + x2

Simplifying
f = 36x-1 + -100i2x-1 + -25i2 + -15 + -2x + x2

Reorder the terms:
f = -15 + -25i2 + -100i2x-1 + 36x-1 + -2x + x2

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