(x-4)(x+1+i)(x-1-i)=0

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Solution for (x-4)(x+1+i)(x-1-i)=0 equation: 


Simplifying
(x + -4)(x + 1 + i)(x + -1 + -1i) = 0

Reorder the terms:
(-4 + x)(x + 1 + i)(x + -1 + -1i) = 0

Reorder the terms:
(-4 + x)(1 + i + x)(x + -1 + -1i) = 0

Reorder the terms:
(-4 + x)(1 + i + x)(-1 + -1i + x) = 0

Multiply (-4 + x) * (1 + i + x)
(-4(1 + i + x) + x(1 + i + x))(-1 + -1i + x) = 0
((1 * -4 + i * -4 + x * -4) + x(1 + i + x))(-1 + -1i + x) = 0
((-4 + -4i + -4x) + x(1 + i + x))(-1 + -1i + x) = 0
(-4 + -4i + -4x + (1 * x + i * x + x * x))(-1 + -1i + x) = 0

Reorder the terms:
(-4 + -4i + -4x + (ix + 1x + x2))(-1 + -1i + x) = 0
(-4 + -4i + -4x + (ix + 1x + x2))(-1 + -1i + x) = 0

Reorder the terms:
(-4 + -4i + ix + -4x + 1x + x2)(-1 + -1i + x) = 0

Combine like terms: -4x + 1x = -3x
(-4 + -4i + ix + -3x + x2)(-1 + -1i + x) = 0

Multiply (-4 + -4i + ix + -3x + x2) * (-1 + -1i + x)
(-4(-1 + -1i + x) + -4i * (-1 + -1i + x) + ix(-1 + -1i + x) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
((-1 * -4 + -1i * -4 + x * -4) + -4i * (-1 + -1i + x) + ix(-1 + -1i + x) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
((4 + 4i + -4x) + -4i * (-1 + -1i + x) + ix(-1 + -1i + x) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(4 + 4i + -4x + (-1 * -4i + -1i * -4i + x * -4i) + ix(-1 + -1i + x) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0

Reorder the terms:
(4 + 4i + -4x + (4i + -4ix + 4i2) + ix(-1 + -1i + x) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(4 + 4i + -4x + (4i + -4ix + 4i2) + ix(-1 + -1i + x) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(4 + 4i + -4x + 4i + -4ix + 4i2 + (-1 * ix + -1i * ix + x * ix) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0

Reorder the terms:
(4 + 4i + -4x + 4i + -4ix + 4i2 + (-1ix + ix2 + -1i2x) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(4 + 4i + -4x + 4i + -4ix + 4i2 + (-1ix + ix2 + -1i2x) + -3x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(4 + 4i + -4x + 4i + -4ix + 4i2 + -1ix + ix2 + -1i2x + (-1 * -3x + -1i * -3x + x * -3x) + x2(-1 + -1i + x)) = 0

Reorder the terms:
(4 + 4i + -4x + 4i + -4ix + 4i2 + -1ix + ix2 + -1i2x + (3ix + 3x + -3x2) + x2(-1 + -1i + x)) = 0
(4 + 4i + -4x + 4i + -4ix + 4i2 + -1ix + ix2 + -1i2x + (3ix + 3x + -3x2) + x2(-1 + -1i + x)) = 0
(4 + 4i + -4x + 4i + -4ix + 4i2 + -1ix + ix2 + -1i2x + 3ix + 3x + -3x2 + (-1 * x2 + -1i * x2 + x * x2)) = 0

Reorder the terms:
(4 + 4i + -4x + 4i + -4ix + 4i2 + -1ix + ix2 + -1i2x + 3ix + 3x + -3x2 + (-1ix2 + -1x2 + x3)) = 0
(4 + 4i + -4x + 4i + -4ix + 4i2 + -1ix + ix2 + -1i2x + 3ix + 3x + -3x2 + (-1ix2 + -1x2 + x3)) = 0

Reorder the terms:
(4 + 4i + 4i + -4ix + -1ix + 3ix + ix2 + -1ix2 + 4i2 + -1i2x + -4x + 3x + -3x2 + -1x2 + x3) = 0

Combine like terms: 4i + 4i = 8i
(4 + 8i + -4ix + -1ix + 3ix + ix2 + -1ix2 + 4i2 + -1i2x + -4x + 3x + -3x2 + -1x2 + x3) = 0

Combine like terms: -4ix + -1ix = -5ix
(4 + 8i + -5ix + 3ix + ix2 + -1ix2 + 4i2 + -1i2x + -4x + 3x + -3x2 + -1x2 + x3) = 0

Combine like terms: -5ix + 3ix = -2ix
(4 + 8i + -2ix + ix2 + -1ix2 + 4i2 + -1i2x + -4x + 3x + -3x2 + -1x2 + x3) = 0

Combine like terms: ix2 + -1ix2 = 0
(4 + 8i + -2ix + 0 + 4i2 + -1i2x + -4x + 3x + -3x2 + -1x2 + x3) = 0
(4 + 8i + -2ix + 4i2 + -1i2x + -4x + 3x + -3x2 + -1x2 + x3) = 0

Combine like terms: -4x + 3x = -1x
(4 + 8i + -2ix + 4i2 + -1i2x + -1x + -3x2 + -1x2 + x3) = 0

Combine like terms: -3x2 + -1x2 = -4x2
(4 + 8i + -2ix + 4i2 + -1i2x + -1x + -4x2 + x3) = 0

Solving
4 + 8i + -2ix + 4i2 + -1i2x + -1x + -4x2 + x3 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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