f(X)=(x-(4+i))(x-(4-i))(x-2)

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Solution for f(X)=(x-(4+i))(x-(4-i))(x-2) equation: 


Simplifying
f(X) = (x + -1(4 + i))(x + -1(4 + -1i))(x + -2)

Multiply f * X
fX = (x + -1(4 + i))(x + -1(4 + -1i))(x + -2)
fX = (x + (4 * -1 + i * -1))(x + -1(4 + -1i))(x + -2)
fX = (x + (-4 + -1i))(x + -1(4 + -1i))(x + -2)

Reorder the terms:
fX = (-4 + -1i + x)(x + -1(4 + -1i))(x + -2)
fX = (-4 + -1i + x)(x + (4 * -1 + -1i * -1))(x + -2)
fX = (-4 + -1i + x)(x + (-4 + 1i))(x + -2)

Reorder the terms:
fX = (-4 + -1i + x)(-4 + 1i + x)(x + -2)

Reorder the terms:
fX = (-4 + -1i + x)(-4 + 1i + x)(-2 + x)

Multiply (-4 + -1i + x) * (-4 + 1i + x)
fX = (-4(-4 + 1i + x) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-2 + x)
fX = ((-4 * -4 + 1i * -4 + x * -4) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-2 + x)
fX = ((16 + -4i + -4x) + -1i * (-4 + 1i + x) + x(-4 + 1i + x))(-2 + x)
fX = (16 + -4i + -4x + (-4 * -1i + 1i * -1i + x * -1i) + x(-4 + 1i + x))(-2 + x)

Reorder the terms:
fX = (16 + -4i + -4x + (4i + -1ix + -1i2) + x(-4 + 1i + x))(-2 + x)
fX = (16 + -4i + -4x + (4i + -1ix + -1i2) + x(-4 + 1i + x))(-2 + x)
fX = (16 + -4i + -4x + 4i + -1ix + -1i2 + (-4 * x + 1i * x + x * x))(-2 + x)

Reorder the terms:
fX = (16 + -4i + -4x + 4i + -1ix + -1i2 + (1ix + -4x + x2))(-2 + x)
fX = (16 + -4i + -4x + 4i + -1ix + -1i2 + (1ix + -4x + x2))(-2 + x)

Reorder the terms:
fX = (16 + -4i + 4i + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-2 + x)

Combine like terms: -4i + 4i = 0
fX = (16 + 0 + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-2 + x)
fX = (16 + -1ix + 1ix + -1i2 + -4x + -4x + x2)(-2 + x)

Combine like terms: -1ix + 1ix = 0
fX = (16 + 0 + -1i2 + -4x + -4x + x2)(-2 + x)
fX = (16 + -1i2 + -4x + -4x + x2)(-2 + x)

Combine like terms: -4x + -4x = -8x
fX = (16 + -1i2 + -8x + x2)(-2 + x)

Multiply (16 + -1i2 + -8x + x2) * (-2 + x)
fX = (16(-2 + x) + -1i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x))
fX = ((-2 * 16 + x * 16) + -1i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x))
fX = ((-32 + 16x) + -1i2 * (-2 + x) + -8x * (-2 + x) + x2(-2 + x))
fX = (-32 + 16x + (-2 * -1i2 + x * -1i2) + -8x * (-2 + x) + x2(-2 + x))
fX = (-32 + 16x + (2i2 + -1i2x) + -8x * (-2 + x) + x2(-2 + x))
fX = (-32 + 16x + 2i2 + -1i2x + (-2 * -8x + x * -8x) + x2(-2 + x))
fX = (-32 + 16x + 2i2 + -1i2x + (16x + -8x2) + x2(-2 + x))
fX = (-32 + 16x + 2i2 + -1i2x + 16x + -8x2 + (-2 * x2 + x * x2))
fX = (-32 + 16x + 2i2 + -1i2x + 16x + -8x2 + (-2x2 + x3))

Reorder the terms:
fX = (-32 + 2i2 + -1i2x + 16x + 16x + -8x2 + -2x2 + x3)

Combine like terms: 16x + 16x = 32x
fX = (-32 + 2i2 + -1i2x + 32x + -8x2 + -2x2 + x3)

Combine like terms: -8x2 + -2x2 = -10x2
fX = (-32 + 2i2 + -1i2x + 32x + -10x2 + x3)

Solving
fX = -32 + 2i2 + -1i2x + 32x + -10x2 + 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 = -32X-1 + 2i2X-1 + -1i2xX-1 + 32xX-1 + -10x2X-1 + x3X-1

Simplifying
f = -32X-1 + 2i2X-1 + -1i2xX-1 + 32xX-1 + -10x2X-1 + x3X-1

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