(x-(2+i))(x-(2-i))=0

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Solution for (x-(2+i))(x-(2-i))=0 equation: 


Simplifying
(x + -1(2 + i))(x + -1(2 + -1i)) = 0
(x + (2 * -1 + i * -1))(x + -1(2 + -1i)) = 0
(x + (-2 + -1i))(x + -1(2 + -1i)) = 0

Reorder the terms:
(-2 + -1i + x)(x + -1(2 + -1i)) = 0
(-2 + -1i + x)(x + (2 * -1 + -1i * -1)) = 0
(-2 + -1i + x)(x + (-2 + 1i)) = 0

Reorder the terms:
(-2 + -1i + x)(-2 + 1i + x) = 0

Multiply (-2 + -1i + x) * (-2 + 1i + x)
(-2(-2 + 1i + x) + -1i * (-2 + 1i + x) + x(-2 + 1i + x)) = 0
((-2 * -2 + 1i * -2 + x * -2) + -1i * (-2 + 1i + x) + x(-2 + 1i + x)) = 0
((4 + -2i + -2x) + -1i * (-2 + 1i + x) + x(-2 + 1i + x)) = 0
(4 + -2i + -2x + (-2 * -1i + 1i * -1i + x * -1i) + x(-2 + 1i + x)) = 0

Reorder the terms:
(4 + -2i + -2x + (2i + -1ix + -1i2) + x(-2 + 1i + x)) = 0
(4 + -2i + -2x + (2i + -1ix + -1i2) + x(-2 + 1i + x)) = 0
(4 + -2i + -2x + 2i + -1ix + -1i2 + (-2 * x + 1i * x + x * x)) = 0

Reorder the terms:
(4 + -2i + -2x + 2i + -1ix + -1i2 + (1ix + -2x + x2)) = 0
(4 + -2i + -2x + 2i + -1ix + -1i2 + (1ix + -2x + x2)) = 0

Reorder the terms:
(4 + -2i + 2i + -1ix + 1ix + -1i2 + -2x + -2x + x2) = 0

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

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

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

Solving
4 + -1i2 + -4x + x2 = 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 + -1i2 + -4x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -1i2 + -4x + x2 = 0 + -4

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

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

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

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

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

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

Divide each side by '-1'.
i2 = 4 + -4x + x2

Simplifying
i2 = 4 + -4x + x2

Reorder the terms:
-4 + i2 + 4x + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2

Reorder the terms:
-4 + i2 + 4x + -1x2 = 4 + -4 + -4x + 4x + x2 + -1x2

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

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

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

The solution to this equation could not be determined.

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