(x+5)(x-[1-i])(x-[1+i])=0

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Solution for (x+5)(x-[1-i])(x-[1+i])=0 equation: 


Simplifying
(x + 5)(x + -1[1 + -1i])(x + -1[1 + i]) = 0

Reorder the terms:
(5 + x)(x + -1[1 + -1i])(x + -1[1 + i]) = 0
(5 + x)(x + [1 * -1 + -1i * -1])(x + -1[1 + i]) = 0
(5 + x)(x + [-1 + 1i])(x + -1[1 + i]) = 0

Reorder the terms:
(5 + x)(-1 + 1i + x)(x + -1[1 + i]) = 0
(5 + x)(-1 + 1i + x)(x + [1 * -1 + i * -1]) = 0
(5 + x)(-1 + 1i + x)(x + [-1 + -1i]) = 0

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

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

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

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

Combine like terms: 5x + -1x = 4x
(-5 + 5i + 1ix + 4x + x2)(-1 + -1i + x) = 0

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

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

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

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

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

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

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

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

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

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

Combine like terms: -5x + -4x = -9x
(5 + -5i2 + -1i2x + -9x + 4x2 + -1x2 + x3) = 0

Combine like terms: 4x2 + -1x2 = 3x2
(5 + -5i2 + -1i2x + -9x + 3x2 + x3) = 0

Solving
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5i2 + -1i2x + -9x + 3x2 + -5 + x3 = 0 + -5

Reorder the terms:
5 + -5 + -5i2 + -1i2x + -9x + 3x2 + x3 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5i2 + -1i2x + -9x + 3x2 + x3 = 0 + -5
-5i2 + -1i2x + -9x + 3x2 + x3 = 0 + -5

Combine like terms: 0 + -5 = -5
-5i2 + -1i2x + -9x + 3x2 + x3 = -5

Add '9x' to each side of the equation.
-5i2 + -1i2x + -9x + 3x2 + 9x + x3 = -5 + 9x

Reorder the terms:
-5i2 + -1i2x + -9x + 9x + 3x2 + x3 = -5 + 9x

Combine like terms: -9x + 9x = 0
-5i2 + -1i2x + 0 + 3x2 + x3 = -5 + 9x
-5i2 + -1i2x + 3x2 + x3 = -5 + 9x

Add '-3x2' to each side of the equation.
-5i2 + -1i2x + 3x2 + -3x2 + x3 = -5 + 9x + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5i2 + -1i2x + 0 + x3 = -5 + 9x + -3x2
-5i2 + -1i2x + x3 = -5 + 9x + -3x2

Add '-1x3' to each side of the equation.
-5i2 + -1i2x + x3 + -1x3 = -5 + 9x + -3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-5i2 + -1i2x + 0 = -5 + 9x + -3x2 + -1x3
-5i2 + -1i2x = -5 + 9x + -3x2 + -1x3

Reorder the terms:
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = -5 + 9x + -3x2 + -1x3 + 5 + -9x + 3x2 + x3

Reorder the terms:
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = -5 + 5 + 9x + -9x + -3x2 + 3x2 + -1x3 + x3

Combine like terms: -5 + 5 = 0
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = 0 + 9x + -9x + -3x2 + 3x2 + -1x3 + x3
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = 9x + -9x + -3x2 + 3x2 + -1x3 + x3

Combine like terms: 9x + -9x = 0
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = 0 + -3x2 + 3x2 + -1x3 + x3
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = -3x2 + 3x2 + -1x3 + x3

Combine like terms: -3x2 + 3x2 = 0
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = 0 + -1x3 + x3
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
5 + -5i2 + -1i2x + -9x + 3x2 + x3 = 0

The solution to this equation could not be determined.

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