f(x)=(x-5)(x-(4-i))(x-(4+i))

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Solution for f(x)=(x-5)(x-(4-i))(x-(4+i)) equation: 


Simplifying
f(x) = (x + -5)(x + -1(4 + -1i))(x + -1(4 + i))

Multiply f * x
fx = (x + -5)(x + -1(4 + -1i))(x + -1(4 + i))

Reorder the terms:
fx = (-5 + x)(x + -1(4 + -1i))(x + -1(4 + i))
fx = (-5 + x)(x + (4 * -1 + -1i * -1))(x + -1(4 + i))
fx = (-5 + x)(x + (-4 + 1i))(x + -1(4 + i))

Reorder the terms:
fx = (-5 + x)(-4 + 1i + x)(x + -1(4 + i))
fx = (-5 + x)(-4 + 1i + x)(x + (4 * -1 + i * -1))
fx = (-5 + x)(-4 + 1i + x)(x + (-4 + -1i))

Reorder the terms:
fx = (-5 + x)(-4 + 1i + x)(-4 + -1i + x)

Multiply (-5 + x) * (-4 + 1i + x)
fx = (-5(-4 + 1i + x) + x(-4 + 1i + x))(-4 + -1i + x)
fx = ((-4 * -5 + 1i * -5 + x * -5) + x(-4 + 1i + x))(-4 + -1i + x)
fx = ((20 + -5i + -5x) + x(-4 + 1i + x))(-4 + -1i + x)
fx = (20 + -5i + -5x + (-4 * x + 1i * x + x * x))(-4 + -1i + x)

Reorder the terms:
fx = (20 + -5i + -5x + (1ix + -4x + x2))(-4 + -1i + x)
fx = (20 + -5i + -5x + (1ix + -4x + x2))(-4 + -1i + x)

Reorder the terms:
fx = (20 + -5i + 1ix + -5x + -4x + x2)(-4 + -1i + x)

Combine like terms: -5x + -4x = -9x
fx = (20 + -5i + 1ix + -9x + x2)(-4 + -1i + x)

Multiply (20 + -5i + 1ix + -9x + x2) * (-4 + -1i + x)
fx = (20(-4 + -1i + x) + -5i * (-4 + -1i + x) + 1ix * (-4 + -1i + x) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))
fx = ((-4 * 20 + -1i * 20 + x * 20) + -5i * (-4 + -1i + x) + 1ix * (-4 + -1i + x) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))
fx = ((-80 + -20i + 20x) + -5i * (-4 + -1i + x) + 1ix * (-4 + -1i + x) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))
fx = (-80 + -20i + 20x + (-4 * -5i + -1i * -5i + x * -5i) + 1ix * (-4 + -1i + x) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))

Reorder the terms:
fx = (-80 + -20i + 20x + (20i + -5ix + 5i2) + 1ix * (-4 + -1i + x) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))
fx = (-80 + -20i + 20x + (20i + -5ix + 5i2) + 1ix * (-4 + -1i + x) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + (-4 * 1ix + -1i * 1ix + x * 1ix) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))

Reorder the terms:
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + (-4ix + 1ix2 + -1i2x) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + (-4ix + 1ix2 + -1i2x) + -9x * (-4 + -1i + x) + x2(-4 + -1i + x))
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + -4ix + 1ix2 + -1i2x + (-4 * -9x + -1i * -9x + x * -9x) + x2(-4 + -1i + x))

Reorder the terms:
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + -4ix + 1ix2 + -1i2x + (9ix + 36x + -9x2) + x2(-4 + -1i + x))
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + -4ix + 1ix2 + -1i2x + (9ix + 36x + -9x2) + x2(-4 + -1i + x))
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + -4ix + 1ix2 + -1i2x + 9ix + 36x + -9x2 + (-4 * x2 + -1i * x2 + x * x2))

Reorder the terms:
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + -4ix + 1ix2 + -1i2x + 9ix + 36x + -9x2 + (-1ix2 + -4x2 + x3))
fx = (-80 + -20i + 20x + 20i + -5ix + 5i2 + -4ix + 1ix2 + -1i2x + 9ix + 36x + -9x2 + (-1ix2 + -4x2 + x3))

Reorder the terms:
fx = (-80 + -20i + 20i + -5ix + -4ix + 9ix + 1ix2 + -1ix2 + 5i2 + -1i2x + 20x + 36x + -9x2 + -4x2 + x3)

Combine like terms: -20i + 20i = 0
fx = (-80 + 0 + -5ix + -4ix + 9ix + 1ix2 + -1ix2 + 5i2 + -1i2x + 20x + 36x + -9x2 + -4x2 + x3)
fx = (-80 + -5ix + -4ix + 9ix + 1ix2 + -1ix2 + 5i2 + -1i2x + 20x + 36x + -9x2 + -4x2 + x3)

Combine like terms: -5ix + -4ix = -9ix
fx = (-80 + -9ix + 9ix + 1ix2 + -1ix2 + 5i2 + -1i2x + 20x + 36x + -9x2 + -4x2 + x3)

Combine like terms: -9ix + 9ix = 0
fx = (-80 + 0 + 1ix2 + -1ix2 + 5i2 + -1i2x + 20x + 36x + -9x2 + -4x2 + x3)
fx = (-80 + 1ix2 + -1ix2 + 5i2 + -1i2x + 20x + 36x + -9x2 + -4x2 + x3)

Combine like terms: 1ix2 + -1ix2 = 0
fx = (-80 + 0 + 5i2 + -1i2x + 20x + 36x + -9x2 + -4x2 + x3)
fx = (-80 + 5i2 + -1i2x + 20x + 36x + -9x2 + -4x2 + x3)

Combine like terms: 20x + 36x = 56x
fx = (-80 + 5i2 + -1i2x + 56x + -9x2 + -4x2 + x3)

Combine like terms: -9x2 + -4x2 = -13x2
fx = (-80 + 5i2 + -1i2x + 56x + -13x2 + x3)

Solving
fx = -80 + 5i2 + -1i2x + 56x + -13x2 + 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 = -80x-1 + 5i2x-1 + -1i2 + 56 + -13x + x2

Simplifying
f = -80x-1 + 5i2x-1 + -1i2 + 56 + -13x + x2

Reorder the terms:
f = 56 + -1i2 + 5i2x-1 + -80x-1 + -13x + x2

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