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

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


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

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

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

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

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

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

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

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

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

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

Combine like terms: -1x + -1x = -2x
(1 + -1i2 + -2x + x2)(-4 + x) = 0

Multiply (1 + -1i2 + -2x + x2) * (-4 + x)
(1(-4 + x) + -1i2 * (-4 + x) + -2x * (-4 + x) + x2(-4 + x)) = 0
((-4 * 1 + x * 1) + -1i2 * (-4 + x) + -2x * (-4 + x) + x2(-4 + x)) = 0
((-4 + 1x) + -1i2 * (-4 + x) + -2x * (-4 + x) + x2(-4 + x)) = 0
(-4 + 1x + (-4 * -1i2 + x * -1i2) + -2x * (-4 + x) + x2(-4 + x)) = 0
(-4 + 1x + (4i2 + -1i2x) + -2x * (-4 + x) + x2(-4 + x)) = 0
(-4 + 1x + 4i2 + -1i2x + (-4 * -2x + x * -2x) + x2(-4 + x)) = 0
(-4 + 1x + 4i2 + -1i2x + (8x + -2x2) + x2(-4 + x)) = 0
(-4 + 1x + 4i2 + -1i2x + 8x + -2x2 + (-4 * x2 + x * x2)) = 0
(-4 + 1x + 4i2 + -1i2x + 8x + -2x2 + (-4x2 + x3)) = 0

Reorder the terms:
(-4 + 4i2 + -1i2x + 1x + 8x + -2x2 + -4x2 + x3) = 0

Combine like terms: 1x + 8x = 9x
(-4 + 4i2 + -1i2x + 9x + -2x2 + -4x2 + x3) = 0

Combine like terms: -2x2 + -4x2 = -6x2
(-4 + 4i2 + -1i2x + 9x + -6x2 + x3) = 0

Solving
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0

Solving for variable 'i'.

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

Add '4' to each side of the equation.
-4 + 4i2 + -1i2x + 9x + -6x2 + 4 + x3 = 0 + 4

Reorder the terms:
-4 + 4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + 4
4i2 + -1i2x + 9x + -6x2 + x3 = 0 + 4

Combine like terms: 0 + 4 = 4
4i2 + -1i2x + 9x + -6x2 + x3 = 4

Add '-9x' to each side of the equation.
4i2 + -1i2x + 9x + -6x2 + -9x + x3 = 4 + -9x

Reorder the terms:
4i2 + -1i2x + 9x + -9x + -6x2 + x3 = 4 + -9x

Combine like terms: 9x + -9x = 0
4i2 + -1i2x + 0 + -6x2 + x3 = 4 + -9x
4i2 + -1i2x + -6x2 + x3 = 4 + -9x

Add '6x2' to each side of the equation.
4i2 + -1i2x + -6x2 + 6x2 + x3 = 4 + -9x + 6x2

Combine like terms: -6x2 + 6x2 = 0
4i2 + -1i2x + 0 + x3 = 4 + -9x + 6x2
4i2 + -1i2x + x3 = 4 + -9x + 6x2

Add '-1x3' to each side of the equation.
4i2 + -1i2x + x3 + -1x3 = 4 + -9x + 6x2 + -1x3

Combine like terms: x3 + -1x3 = 0
4i2 + -1i2x + 0 = 4 + -9x + 6x2 + -1x3
4i2 + -1i2x = 4 + -9x + 6x2 + -1x3

Reorder the terms:
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 4 + -9x + 6x2 + -1x3 + -4 + 9x + -6x2 + x3

Reorder the terms:
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 4 + -4 + -9x + 9x + 6x2 + -6x2 + -1x3 + x3

Combine like terms: 4 + -4 = 0
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + -9x + 9x + 6x2 + -6x2 + -1x3 + x3
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = -9x + 9x + 6x2 + -6x2 + -1x3 + x3

Combine like terms: -9x + 9x = 0
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + 6x2 + -6x2 + -1x3 + x3
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 6x2 + -6x2 + -1x3 + x3

Combine like terms: 6x2 + -6x2 = 0
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0 + -1x3 + x3
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-4 + 4i2 + -1i2x + 9x + -6x2 + x3 = 0

The solution to this equation could not be determined.

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