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

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


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

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

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

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

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

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

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

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

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

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

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

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

Multiply (16 + -1i2 + -8x + x2) * (-1 + x)
fx = (16(-1 + x) + -1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x))
fx = ((-1 * 16 + x * 16) + -1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x))
fx = ((-16 + 16x) + -1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x))
fx = (-16 + 16x + (-1 * -1i2 + x * -1i2) + -8x * (-1 + x) + x2(-1 + x))
fx = (-16 + 16x + (1i2 + -1i2x) + -8x * (-1 + x) + x2(-1 + x))
fx = (-16 + 16x + 1i2 + -1i2x + (-1 * -8x + x * -8x) + x2(-1 + x))
fx = (-16 + 16x + 1i2 + -1i2x + (8x + -8x2) + x2(-1 + x))
fx = (-16 + 16x + 1i2 + -1i2x + 8x + -8x2 + (-1 * x2 + x * x2))
fx = (-16 + 16x + 1i2 + -1i2x + 8x + -8x2 + (-1x2 + x3))

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

Combine like terms: 16x + 8x = 24x
fx = (-16 + 1i2 + -1i2x + 24x + -8x2 + -1x2 + x3)

Combine like terms: -8x2 + -1x2 = -9x2
fx = (-16 + 1i2 + -1i2x + 24x + -9x2 + x3)

Solving
fx = -16 + 1i2 + -1i2x + 24x + -9x2 + 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 = -16x-1 + i2x-1 + -1i2 + 24 + -9x + x2

Simplifying
f = -16x-1 + i2x-1 + -1i2 + 24 + -9x + x2

Reorder the terms:
f = 24 + -1i2 + i2x-1 + -16x-1 + -9x + x2

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