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

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


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

Remove parenthesis around (2 + i)
(x + 2 + i)(x + (2 + -1i)) = 0

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

Remove parenthesis around (2 + -1i)
(2 + i + x)(x + 2 + -1i) = 0

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

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

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

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

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

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

Combine like terms: ix + -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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