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

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


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

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

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

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

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

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

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

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

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

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

Solving
9 + -1i2 + -6x + x2 = 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 + -6x + -9 + x2 = 0 + -9

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

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

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

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

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

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

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

Divide each side by '-1'.
i2 = 9 + -6x + x2

Simplifying
i2 = 9 + -6x + x2

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

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

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

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

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

The solution to this equation could not be determined.

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