f(x)=(x+2)(x-5-2i)(x-5+2i)

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Solution for f(x)=(x+2)(x-5-2i)(x-5+2i) equation: 


Simplifying
f(x) = (x + 2)(x + -5 + -2i)(x + -5 + 2i)

Multiply f * x
fx = (x + 2)(x + -5 + -2i)(x + -5 + 2i)

Reorder the terms:
fx = (2 + x)(x + -5 + -2i)(x + -5 + 2i)

Reorder the terms:
fx = (2 + x)(-5 + -2i + x)(x + -5 + 2i)

Reorder the terms:
fx = (2 + x)(-5 + -2i + x)(-5 + 2i + x)

Multiply (2 + x) * (-5 + -2i + x)
fx = (2(-5 + -2i + x) + x(-5 + -2i + x))(-5 + 2i + x)
fx = ((-5 * 2 + -2i * 2 + x * 2) + x(-5 + -2i + x))(-5 + 2i + x)
fx = ((-10 + -4i + 2x) + x(-5 + -2i + x))(-5 + 2i + x)
fx = (-10 + -4i + 2x + (-5 * x + -2i * x + x * x))(-5 + 2i + x)

Reorder the terms:
fx = (-10 + -4i + 2x + (-2ix + -5x + x2))(-5 + 2i + x)
fx = (-10 + -4i + 2x + (-2ix + -5x + x2))(-5 + 2i + x)

Reorder the terms:
fx = (-10 + -4i + -2ix + 2x + -5x + x2)(-5 + 2i + x)

Combine like terms: 2x + -5x = -3x
fx = (-10 + -4i + -2ix + -3x + x2)(-5 + 2i + x)

Multiply (-10 + -4i + -2ix + -3x + x2) * (-5 + 2i + x)
fx = (-10(-5 + 2i + x) + -4i * (-5 + 2i + x) + -2ix * (-5 + 2i + x) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))
fx = ((-5 * -10 + 2i * -10 + x * -10) + -4i * (-5 + 2i + x) + -2ix * (-5 + 2i + x) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))
fx = ((50 + -20i + -10x) + -4i * (-5 + 2i + x) + -2ix * (-5 + 2i + x) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))
fx = (50 + -20i + -10x + (-5 * -4i + 2i * -4i + x * -4i) + -2ix * (-5 + 2i + x) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))

Reorder the terms:
fx = (50 + -20i + -10x + (20i + -4ix + -8i2) + -2ix * (-5 + 2i + x) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))
fx = (50 + -20i + -10x + (20i + -4ix + -8i2) + -2ix * (-5 + 2i + x) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + (-5 * -2ix + 2i * -2ix + x * -2ix) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))

Reorder the terms:
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + (10ix + -2ix2 + -4i2x) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + (10ix + -2ix2 + -4i2x) + -3x * (-5 + 2i + x) + x2(-5 + 2i + x))
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + 10ix + -2ix2 + -4i2x + (-5 * -3x + 2i * -3x + x * -3x) + x2(-5 + 2i + x))

Reorder the terms:
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + 10ix + -2ix2 + -4i2x + (-6ix + 15x + -3x2) + x2(-5 + 2i + x))
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + 10ix + -2ix2 + -4i2x + (-6ix + 15x + -3x2) + x2(-5 + 2i + x))
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + 10ix + -2ix2 + -4i2x + -6ix + 15x + -3x2 + (-5 * x2 + 2i * x2 + x * x2))

Reorder the terms:
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + 10ix + -2ix2 + -4i2x + -6ix + 15x + -3x2 + (2ix2 + -5x2 + x3))
fx = (50 + -20i + -10x + 20i + -4ix + -8i2 + 10ix + -2ix2 + -4i2x + -6ix + 15x + -3x2 + (2ix2 + -5x2 + x3))

Reorder the terms:
fx = (50 + -20i + 20i + -4ix + 10ix + -6ix + -2ix2 + 2ix2 + -8i2 + -4i2x + -10x + 15x + -3x2 + -5x2 + x3)

Combine like terms: -20i + 20i = 0
fx = (50 + 0 + -4ix + 10ix + -6ix + -2ix2 + 2ix2 + -8i2 + -4i2x + -10x + 15x + -3x2 + -5x2 + x3)
fx = (50 + -4ix + 10ix + -6ix + -2ix2 + 2ix2 + -8i2 + -4i2x + -10x + 15x + -3x2 + -5x2 + x3)

Combine like terms: -4ix + 10ix = 6ix
fx = (50 + 6ix + -6ix + -2ix2 + 2ix2 + -8i2 + -4i2x + -10x + 15x + -3x2 + -5x2 + x3)

Combine like terms: 6ix + -6ix = 0
fx = (50 + 0 + -2ix2 + 2ix2 + -8i2 + -4i2x + -10x + 15x + -3x2 + -5x2 + x3)
fx = (50 + -2ix2 + 2ix2 + -8i2 + -4i2x + -10x + 15x + -3x2 + -5x2 + x3)

Combine like terms: -2ix2 + 2ix2 = 0
fx = (50 + 0 + -8i2 + -4i2x + -10x + 15x + -3x2 + -5x2 + x3)
fx = (50 + -8i2 + -4i2x + -10x + 15x + -3x2 + -5x2 + x3)

Combine like terms: -10x + 15x = 5x
fx = (50 + -8i2 + -4i2x + 5x + -3x2 + -5x2 + x3)

Combine like terms: -3x2 + -5x2 = -8x2
fx = (50 + -8i2 + -4i2x + 5x + -8x2 + x3)

Solving
fx = 50 + -8i2 + -4i2x + 5x + -8x2 + 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 = 50x-1 + -8i2x-1 + -4i2 + 5 + -8x + x2

Simplifying
f = 50x-1 + -8i2x-1 + -4i2 + 5 + -8x + x2

Reorder the terms:
f = 5 + -4i2 + -8i2x-1 + 50x-1 + -8x + x2

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