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

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


Simplifying
f(x) = (x + -2)[x + -1(2 + -5i)][x + -1(2 + 5i)]

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

Reorder the terms:
fx = (-2 + x)[x + -1(2 + -5i)][x + -1(2 + 5i)]
fx = (-2 + x)[x + (2 * -1 + -5i * -1)][x + -1(2 + 5i)]
fx = (-2 + x)[x + (-2 + 5i)][x + -1(2 + 5i)]

Reorder the terms:
fx = (-2 + x)[-2 + 5i + x][x + -1(2 + 5i)]
fx = (-2 + x)[-2 + 5i + x][x + (2 * -1 + 5i * -1)]
fx = (-2 + x)[-2 + 5i + x][x + (-2 + -5i)]

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

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

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

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

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

Multiply (4 + -10i + 5ix + -4x + x2) * [-2 + -5i + x]
fx = (4[-2 + -5i + x] + -10i * [-2 + -5i + x] + 5ix * [-2 + -5i + x] + -4x * [-2 + -5i + x] + x2[-2 + -5i + x])
fx = ([-2 * 4 + -5i * 4 + x * 4] + -10i * [-2 + -5i + x] + 5ix * [-2 + -5i + x] + -4x * [-2 + -5i + x] + x2[-2 + -5i + x])
fx = ([-8 + -20i + 4x] + -10i * [-2 + -5i + x] + 5ix * [-2 + -5i + x] + -4x * [-2 + -5i + x] + x2[-2 + -5i + x])
fx = (-8 + -20i + 4x + [-2 * -10i + -5i * -10i + x * -10i] + 5ix * [-2 + -5i + x] + -4x * [-2 + -5i + x] + x2[-2 + -5i + x])

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

Reorder the terms:
fx = (-8 + -20i + 4x + 20i + -10ix + 50i2 + [-10ix + 5ix2 + -25i2x] + -4x * [-2 + -5i + x] + x2[-2 + -5i + x])
fx = (-8 + -20i + 4x + 20i + -10ix + 50i2 + [-10ix + 5ix2 + -25i2x] + -4x * [-2 + -5i + x] + x2[-2 + -5i + x])
fx = (-8 + -20i + 4x + 20i + -10ix + 50i2 + -10ix + 5ix2 + -25i2x + [-2 * -4x + -5i * -4x + x * -4x] + x2[-2 + -5i + x])

Reorder the terms:
fx = (-8 + -20i + 4x + 20i + -10ix + 50i2 + -10ix + 5ix2 + -25i2x + [20ix + 8x + -4x2] + x2[-2 + -5i + x])
fx = (-8 + -20i + 4x + 20i + -10ix + 50i2 + -10ix + 5ix2 + -25i2x + [20ix + 8x + -4x2] + x2[-2 + -5i + x])
fx = (-8 + -20i + 4x + 20i + -10ix + 50i2 + -10ix + 5ix2 + -25i2x + 20ix + 8x + -4x2 + [-2 * x2 + -5i * x2 + x * x2])

Reorder the terms:
fx = (-8 + -20i + 4x + 20i + -10ix + 50i2 + -10ix + 5ix2 + -25i2x + 20ix + 8x + -4x2 + [-5ix2 + -2x2 + x3])
fx = (-8 + -20i + 4x + 20i + -10ix + 50i2 + -10ix + 5ix2 + -25i2x + 20ix + 8x + -4x2 + [-5ix2 + -2x2 + x3])

Reorder the terms:
fx = (-8 + -20i + 20i + -10ix + -10ix + 20ix + 5ix2 + -5ix2 + 50i2 + -25i2x + 4x + 8x + -4x2 + -2x2 + x3)

Combine like terms: -20i + 20i = 0
fx = (-8 + 0 + -10ix + -10ix + 20ix + 5ix2 + -5ix2 + 50i2 + -25i2x + 4x + 8x + -4x2 + -2x2 + x3)
fx = (-8 + -10ix + -10ix + 20ix + 5ix2 + -5ix2 + 50i2 + -25i2x + 4x + 8x + -4x2 + -2x2 + x3)

Combine like terms: -10ix + -10ix = -20ix
fx = (-8 + -20ix + 20ix + 5ix2 + -5ix2 + 50i2 + -25i2x + 4x + 8x + -4x2 + -2x2 + x3)

Combine like terms: -20ix + 20ix = 0
fx = (-8 + 0 + 5ix2 + -5ix2 + 50i2 + -25i2x + 4x + 8x + -4x2 + -2x2 + x3)
fx = (-8 + 5ix2 + -5ix2 + 50i2 + -25i2x + 4x + 8x + -4x2 + -2x2 + x3)

Combine like terms: 5ix2 + -5ix2 = 0
fx = (-8 + 0 + 50i2 + -25i2x + 4x + 8x + -4x2 + -2x2 + x3)
fx = (-8 + 50i2 + -25i2x + 4x + 8x + -4x2 + -2x2 + x3)

Combine like terms: 4x + 8x = 12x
fx = (-8 + 50i2 + -25i2x + 12x + -4x2 + -2x2 + x3)

Combine like terms: -4x2 + -2x2 = -6x2
fx = (-8 + 50i2 + -25i2x + 12x + -6x2 + x3)

Solving
fx = -8 + 50i2 + -25i2x + 12x + -6x2 + 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 = -8x-1 + 50i2x-1 + -25i2 + 12 + -6x + x2

Simplifying
f = -8x-1 + 50i2x-1 + -25i2 + 12 + -6x + x2

Reorder the terms:
f = 12 + -25i2 + 50i2x-1 + -8x-1 + -6x + x2

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