f(x)=(x-1+i)(x-1-i)(x-4)

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Solution for f(x)=(x-1+i)(x-1-i)(x-4) equation: 


Simplifying
f(x) = (x + -1 + i)(x + -1 + -1i)(x + -4)

Multiply f * x
fx = (x + -1 + i)(x + -1 + -1i)(x + -4)

Reorder the terms:
fx = (-1 + i + x)(x + -1 + -1i)(x + -4)

Reorder the terms:
fx = (-1 + i + x)(-1 + -1i + x)(x + -4)

Reorder the terms:
fx = (-1 + i + x)(-1 + -1i + x)(-4 + x)

Multiply (-1 + i + x) * (-1 + -1i + x)
fx = (-1(-1 + -1i + x) + i(-1 + -1i + x) + x(-1 + -1i + x))(-4 + x)
fx = ((-1 * -1 + -1i * -1 + x * -1) + i(-1 + -1i + x) + x(-1 + -1i + x))(-4 + x)
fx = ((1 + 1i + -1x) + i(-1 + -1i + x) + x(-1 + -1i + x))(-4 + x)
fx = (1 + 1i + -1x + (-1 * i + -1i * i + x * i) + x(-1 + -1i + x))(-4 + x)

Reorder the terms:
fx = (1 + 1i + -1x + (-1i + ix + -1i2) + x(-1 + -1i + x))(-4 + x)
fx = (1 + 1i + -1x + (-1i + ix + -1i2) + x(-1 + -1i + x))(-4 + x)
fx = (1 + 1i + -1x + -1i + ix + -1i2 + (-1 * x + -1i * x + x * x))(-4 + x)

Reorder the terms:
fx = (1 + 1i + -1x + -1i + ix + -1i2 + (-1ix + -1x + x2))(-4 + x)
fx = (1 + 1i + -1x + -1i + ix + -1i2 + (-1ix + -1x + x2))(-4 + x)

Reorder the terms:
fx = (1 + 1i + -1i + ix + -1ix + -1i2 + -1x + -1x + x2)(-4 + x)

Combine like terms: 1i + -1i = 0
fx = (1 + 0 + ix + -1ix + -1i2 + -1x + -1x + x2)(-4 + x)
fx = (1 + ix + -1ix + -1i2 + -1x + -1x + x2)(-4 + x)

Combine like terms: ix + -1ix = 0
fx = (1 + 0 + -1i2 + -1x + -1x + x2)(-4 + x)
fx = (1 + -1i2 + -1x + -1x + x2)(-4 + x)

Combine like terms: -1x + -1x = -2x
fx = (1 + -1i2 + -2x + x2)(-4 + x)

Multiply (1 + -1i2 + -2x + x2) * (-4 + x)
fx = (1(-4 + x) + -1i2 * (-4 + x) + -2x * (-4 + x) + x2(-4 + x))
fx = ((-4 * 1 + x * 1) + -1i2 * (-4 + x) + -2x * (-4 + x) + x2(-4 + x))
fx = ((-4 + 1x) + -1i2 * (-4 + x) + -2x * (-4 + x) + x2(-4 + x))
fx = (-4 + 1x + (-4 * -1i2 + x * -1i2) + -2x * (-4 + x) + x2(-4 + x))
fx = (-4 + 1x + (4i2 + -1i2x) + -2x * (-4 + x) + x2(-4 + x))
fx = (-4 + 1x + 4i2 + -1i2x + (-4 * -2x + x * -2x) + x2(-4 + x))
fx = (-4 + 1x + 4i2 + -1i2x + (8x + -2x2) + x2(-4 + x))
fx = (-4 + 1x + 4i2 + -1i2x + 8x + -2x2 + (-4 * x2 + x * x2))
fx = (-4 + 1x + 4i2 + -1i2x + 8x + -2x2 + (-4x2 + x3))

Reorder the terms:
fx = (-4 + 4i2 + -1i2x + 1x + 8x + -2x2 + -4x2 + x3)

Combine like terms: 1x + 8x = 9x
fx = (-4 + 4i2 + -1i2x + 9x + -2x2 + -4x2 + x3)

Combine like terms: -2x2 + -4x2 = -6x2
fx = (-4 + 4i2 + -1i2x + 9x + -6x2 + x3)

Solving
fx = -4 + 4i2 + -1i2x + 9x + -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 = -4x-1 + 4i2x-1 + -1i2 + 9 + -6x + x2

Simplifying
f = -4x-1 + 4i2x-1 + -1i2 + 9 + -6x + x2

Reorder the terms:
f = 9 + -1i2 + 4i2x-1 + -4x-1 + -6x + x2

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