(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 = 5x
(4 + 4i + ix + 5x + x2)(-1 + -1i + x) = 0

Multiply (4 + 4i + ix + 5x + x2) * (-1 + -1i + x)
(4(-1 + -1i + x) + 4i * (-1 + -1i + x) + ix(-1 + -1i + x) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
((-1 * 4 + -1i * 4 + x * 4) + 4i * (-1 + -1i + x) + ix(-1 + -1i + x) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
((-4 + -4i + 4x) + 4i * (-1 + -1i + x) + ix(-1 + -1i + x) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(-4 + -4i + 4x + (-1 * 4i + -1i * 4i + x * 4i) + ix(-1 + -1i + x) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0

Reorder the terms:
(-4 + -4i + 4x + (-4i + 4ix + -4i2) + ix(-1 + -1i + x) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(-4 + -4i + 4x + (-4i + 4ix + -4i2) + ix(-1 + -1i + x) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(-4 + -4i + 4x + -4i + 4ix + -4i2 + (-1 * ix + -1i * ix + x * ix) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0

Reorder the terms:
(-4 + -4i + 4x + -4i + 4ix + -4i2 + (-1ix + ix2 + -1i2x) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(-4 + -4i + 4x + -4i + 4ix + -4i2 + (-1ix + ix2 + -1i2x) + 5x * (-1 + -1i + x) + x2(-1 + -1i + x)) = 0
(-4 + -4i + 4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + (-1 * 5x + -1i * 5x + x * 5x) + x2(-1 + -1i + x)) = 0

Reorder the terms:
(-4 + -4i + 4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + (-5ix + -5x + 5x2) + x2(-1 + -1i + x)) = 0
(-4 + -4i + 4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + (-5ix + -5x + 5x2) + x2(-1 + -1i + x)) = 0
(-4 + -4i + 4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + -5ix + -5x + 5x2 + (-1 * x2 + -1i * x2 + x * x2)) = 0

Reorder the terms:
(-4 + -4i + 4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + -5ix + -5x + 5x2 + (-1ix2 + -1x2 + x3)) = 0
(-4 + -4i + 4x + -4i + 4ix + -4i2 + -1ix + ix2 + -1i2x + -5ix + -5x + 5x2 + (-1ix2 + -1x2 + x3)) = 0

Reorder the terms:
(-4 + -4i + -4i + 4ix + -1ix + -5ix + ix2 + -1ix2 + -4i2 + -1i2x + 4x + -5x + 5x2 + -1x2 + x3) = 0

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

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

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

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

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

Combine like terms: 5x2 + -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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