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

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


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

Remove parenthesis around (3 + -1i)
(x + 3 + -1i)(x + (3 + i))(x + -3) = 0

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

Remove parenthesis around (3 + i)
(3 + -1i + x)(x + 3 + i)(x + -3) = 0

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

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

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

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

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

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

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

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

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

Multiply (9 + -1i2 + 6x + x2) * (-3 + x)
(9(-3 + x) + -1i2 * (-3 + x) + 6x * (-3 + x) + x2(-3 + x)) = 0
((-3 * 9 + x * 9) + -1i2 * (-3 + x) + 6x * (-3 + x) + x2(-3 + x)) = 0
((-27 + 9x) + -1i2 * (-3 + x) + 6x * (-3 + x) + x2(-3 + x)) = 0
(-27 + 9x + (-3 * -1i2 + x * -1i2) + 6x * (-3 + x) + x2(-3 + x)) = 0
(-27 + 9x + (3i2 + -1i2x) + 6x * (-3 + x) + x2(-3 + x)) = 0
(-27 + 9x + 3i2 + -1i2x + (-3 * 6x + x * 6x) + x2(-3 + x)) = 0
(-27 + 9x + 3i2 + -1i2x + (-18x + 6x2) + x2(-3 + x)) = 0
(-27 + 9x + 3i2 + -1i2x + -18x + 6x2 + (-3 * x2 + x * x2)) = 0
(-27 + 9x + 3i2 + -1i2x + -18x + 6x2 + (-3x2 + x3)) = 0

Reorder the terms:
(-27 + 3i2 + -1i2x + 9x + -18x + 6x2 + -3x2 + x3) = 0

Combine like terms: 9x + -18x = -9x
(-27 + 3i2 + -1i2x + -9x + 6x2 + -3x2 + x3) = 0

Combine like terms: 6x2 + -3x2 = 3x2
(-27 + 3i2 + -1i2x + -9x + 3x2 + x3) = 0

Solving
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 0

Solving for variable 'i'.

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

Add '27' to each side of the equation.
-27 + 3i2 + -1i2x + -9x + 3x2 + 27 + x3 = 0 + 27

Reorder the terms:
-27 + 27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 3i2 + -1i2x + -9x + 3x2 + x3 = 0 + 27
3i2 + -1i2x + -9x + 3x2 + x3 = 0 + 27

Combine like terms: 0 + 27 = 27
3i2 + -1i2x + -9x + 3x2 + x3 = 27

Add '9x' to each side of the equation.
3i2 + -1i2x + -9x + 3x2 + 9x + x3 = 27 + 9x

Reorder the terms:
3i2 + -1i2x + -9x + 9x + 3x2 + x3 = 27 + 9x

Combine like terms: -9x + 9x = 0
3i2 + -1i2x + 0 + 3x2 + x3 = 27 + 9x
3i2 + -1i2x + 3x2 + x3 = 27 + 9x

Add '-3x2' to each side of the equation.
3i2 + -1i2x + 3x2 + -3x2 + x3 = 27 + 9x + -3x2

Combine like terms: 3x2 + -3x2 = 0
3i2 + -1i2x + 0 + x3 = 27 + 9x + -3x2
3i2 + -1i2x + x3 = 27 + 9x + -3x2

Add '-1x3' to each side of the equation.
3i2 + -1i2x + x3 + -1x3 = 27 + 9x + -3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
3i2 + -1i2x + 0 = 27 + 9x + -3x2 + -1x3
3i2 + -1i2x = 27 + 9x + -3x2 + -1x3

Reorder the terms:
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 27 + 9x + -3x2 + -1x3 + -27 + -9x + 3x2 + x3

Reorder the terms:
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 27 + -27 + 9x + -9x + -3x2 + 3x2 + -1x3 + x3

Combine like terms: 27 + -27 = 0
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 0 + 9x + -9x + -3x2 + 3x2 + -1x3 + x3
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 9x + -9x + -3x2 + 3x2 + -1x3 + x3

Combine like terms: 9x + -9x = 0
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 0 + -3x2 + 3x2 + -1x3 + x3
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = -3x2 + 3x2 + -1x3 + x3

Combine like terms: -3x2 + 3x2 = 0
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 0 + -1x3 + x3
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-27 + 3i2 + -1i2x + -9x + 3x2 + x3 = 0

The solution to this equation could not be determined.

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