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

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


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

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

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

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

Multiply (-5 + 2i + x) * (-5 + -2i + x)
fx = (-5(-5 + -2i + x) + 2i * (-5 + -2i + x) + x(-5 + -2i + x))
fx = ((-5 * -5 + -2i * -5 + x * -5) + 2i * (-5 + -2i + x) + x(-5 + -2i + x))
fx = ((25 + 10i + -5x) + 2i * (-5 + -2i + x) + x(-5 + -2i + x))
fx = (25 + 10i + -5x + (-5 * 2i + -2i * 2i + x * 2i) + x(-5 + -2i + x))

Reorder the terms:
fx = (25 + 10i + -5x + (-10i + 2ix + -4i2) + x(-5 + -2i + x))
fx = (25 + 10i + -5x + (-10i + 2ix + -4i2) + x(-5 + -2i + x))
fx = (25 + 10i + -5x + -10i + 2ix + -4i2 + (-5 * x + -2i * x + x * x))

Reorder the terms:
fx = (25 + 10i + -5x + -10i + 2ix + -4i2 + (-2ix + -5x + x2))
fx = (25 + 10i + -5x + -10i + 2ix + -4i2 + (-2ix + -5x + x2))

Reorder the terms:
fx = (25 + 10i + -10i + 2ix + -2ix + -4i2 + -5x + -5x + x2)

Combine like terms: 10i + -10i = 0
fx = (25 + 0 + 2ix + -2ix + -4i2 + -5x + -5x + x2)
fx = (25 + 2ix + -2ix + -4i2 + -5x + -5x + x2)

Combine like terms: 2ix + -2ix = 0
fx = (25 + 0 + -4i2 + -5x + -5x + x2)
fx = (25 + -4i2 + -5x + -5x + x2)

Combine like terms: -5x + -5x = -10x
fx = (25 + -4i2 + -10x + x2)

Solving
fx = 25 + -4i2 + -10x + x2

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.
f = 25x-1 + -4i2x-1 + -10 + x

Simplifying
f = 25x-1 + -4i2x-1 + -10 + x

Reorder the terms:
f = -10 + -4i2x-1 + 25x-1 + x

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