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

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


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

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

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

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

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

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

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

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

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

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

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

Solving
fx = 4 + -25i2 + -4x + 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 = 4x-1 + -25i2x-1 + -4 + x

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

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

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