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

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Solution for (x-(1+2i))(x-(1-2i))=0 equation: 


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

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

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

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

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

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

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

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

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

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

Solving
1 + -4i2 + -2x + x2 = 0

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + -4i2 + -2x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -4i2 + -2x + x2 = 0 + -1

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

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

Add '2x' to each side of the equation.
-4i2 + -2x + 2x + x2 = -1 + 2x

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

Add '-1x2' to each side of the equation.
-4i2 + x2 + -1x2 = -1 + 2x + -1x2

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

Divide each side by '-4'.
i2 = 0.25 + -0.5x + 0.25x2

Simplifying
i2 = 0.25 + -0.5x + 0.25x2

Reorder the terms:
-0.25 + i2 + 0.5x + -0.25x2 = 0.25 + -0.5x + 0.25x2 + -0.25 + 0.5x + -0.25x2

Reorder the terms:
-0.25 + i2 + 0.5x + -0.25x2 = 0.25 + -0.25 + -0.5x + 0.5x + 0.25x2 + -0.25x2

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + i2 + 0.5x + -0.25x2 = 0.00 + -0.5x + 0.5x + 0.25x2 + -0.25x2
-0.25 + i2 + 0.5x + -0.25x2 = -0.5x + 0.5x + 0.25x2 + -0.25x2

Combine like terms: -0.5x + 0.5x = 0.0
-0.25 + i2 + 0.5x + -0.25x2 = 0.0 + 0.25x2 + -0.25x2
-0.25 + i2 + 0.5x + -0.25x2 = 0.25x2 + -0.25x2

Combine like terms: 0.25x2 + -0.25x2 = 0.00
-0.25 + i2 + 0.5x + -0.25x2 = 0.00

The solution to this equation could not be determined.

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