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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