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 + -1(2 + 5i)][x + (2 + 5i)]

Multiply f * x
fx = [x + -1(2 + 5i)][x + (2 + 5i)]
fx = [x + (2 * -1 + 5i * -1)][x + (2 + 5i)]
fx = [x + (-2 + -5i)][x + (2 + 5i)]

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

Remove parenthesis around (2 + 5i)
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 = -20i
fx = [-4 + -20i + -5ix + 5ix + -25i2 + -2x + 2x + x2]

Combine like terms: -5ix + 5ix = 0
fx = [-4 + -20i + 0 + -25i2 + -2x + 2x + x2]
fx = [-4 + -20i + -25i2 + -2x + 2x + x2]

Combine like terms: -2x + 2x = 0
fx = [-4 + -20i + -25i2 + 0 + x2]
fx = [-4 + -20i + -25i2 + x2]

Solving
fx = -4 + -20i + -25i2 + 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 + -20ix-1 + -25i2x-1 + x

Simplifying
f = -4x-1 + -20ix-1 + -25i2x-1 + x

Reorder the terms:
f = -20ix-1 + -25i2x-1 + -4x-1 + x

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