(x-(3+i))(x-(3-i))(x+1)=0

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Solution for (x-(3+i))(x-(3-i))(x+1)=0 equation: 


Simplifying
(x + -1(3 + i))(x + -1(3 + -1i))(x + 1) = 0
(x + (3 * -1 + i * -1))(x + -1(3 + -1i))(x + 1) = 0
(x + (-3 + -1i))(x + -1(3 + -1i))(x + 1) = 0

Reorder the terms:
(-3 + -1i + x)(x + -1(3 + -1i))(x + 1) = 0
(-3 + -1i + x)(x + (3 * -1 + -1i * -1))(x + 1) = 0
(-3 + -1i + x)(x + (-3 + 1i))(x + 1) = 0

Reorder the terms:
(-3 + -1i + x)(-3 + 1i + x)(x + 1) = 0

Reorder the terms:
(-3 + -1i + x)(-3 + 1i + x)(1 + x) = 0

Multiply (-3 + -1i + x) * (-3 + 1i + x)
(-3(-3 + 1i + x) + -1i * (-3 + 1i + x) + x(-3 + 1i + x))(1 + x) = 0
((-3 * -3 + 1i * -3 + x * -3) + -1i * (-3 + 1i + x) + x(-3 + 1i + x))(1 + x) = 0
((9 + -3i + -3x) + -1i * (-3 + 1i + x) + x(-3 + 1i + x))(1 + x) = 0
(9 + -3i + -3x + (-3 * -1i + 1i * -1i + x * -1i) + x(-3 + 1i + x))(1 + x) = 0

Reorder the terms:
(9 + -3i + -3x + (3i + -1ix + -1i2) + x(-3 + 1i + x))(1 + x) = 0
(9 + -3i + -3x + (3i + -1ix + -1i2) + x(-3 + 1i + x))(1 + x) = 0
(9 + -3i + -3x + 3i + -1ix + -1i2 + (-3 * x + 1i * x + x * x))(1 + x) = 0

Reorder the terms:
(9 + -3i + -3x + 3i + -1ix + -1i2 + (1ix + -3x + x2))(1 + x) = 0
(9 + -3i + -3x + 3i + -1ix + -1i2 + (1ix + -3x + x2))(1 + x) = 0

Reorder the terms:
(9 + -3i + 3i + -1ix + 1ix + -1i2 + -3x + -3x + x2)(1 + x) = 0

Combine like terms: -3i + 3i = 0
(9 + 0 + -1ix + 1ix + -1i2 + -3x + -3x + x2)(1 + x) = 0
(9 + -1ix + 1ix + -1i2 + -3x + -3x + x2)(1 + x) = 0

Combine like terms: -1ix + 1ix = 0
(9 + 0 + -1i2 + -3x + -3x + x2)(1 + x) = 0
(9 + -1i2 + -3x + -3x + x2)(1 + x) = 0

Combine like terms: -3x + -3x = -6x
(9 + -1i2 + -6x + x2)(1 + x) = 0

Multiply (9 + -1i2 + -6x + x2) * (1 + x)
(9(1 + x) + -1i2 * (1 + x) + -6x * (1 + x) + x2(1 + x)) = 0
((1 * 9 + x * 9) + -1i2 * (1 + x) + -6x * (1 + x) + x2(1 + x)) = 0
((9 + 9x) + -1i2 * (1 + x) + -6x * (1 + x) + x2(1 + x)) = 0
(9 + 9x + (1 * -1i2 + x * -1i2) + -6x * (1 + x) + x2(1 + x)) = 0
(9 + 9x + (-1i2 + -1i2x) + -6x * (1 + x) + x2(1 + x)) = 0
(9 + 9x + -1i2 + -1i2x + (1 * -6x + x * -6x) + x2(1 + x)) = 0
(9 + 9x + -1i2 + -1i2x + (-6x + -6x2) + x2(1 + x)) = 0
(9 + 9x + -1i2 + -1i2x + -6x + -6x2 + (1 * x2 + x * x2)) = 0
(9 + 9x + -1i2 + -1i2x + -6x + -6x2 + (1x2 + x3)) = 0

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

Combine like terms: 9x + -6x = 3x
(9 + -1i2 + -1i2x + 3x + -6x2 + 1x2 + x3) = 0

Combine like terms: -6x2 + 1x2 = -5x2
(9 + -1i2 + -1i2x + 3x + -5x2 + x3) = 0

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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