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

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


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

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

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

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

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

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x))(2i + x)(-2i + x) = 0
((-1 * -1 + x * -1) + x(-1 + x))(2i + x)(-2i + x) = 0
((1 + -1x) + x(-1 + x))(2i + x)(-2i + x) = 0
(1 + -1x + (-1 * x + x * x))(2i + x)(-2i + x) = 0
(1 + -1x + (-1x + x2))(2i + x)(-2i + x) = 0

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

Multiply (1 + -2x + x2) * (2i + x)
(1(2i + x) + -2x * (2i + x) + x2(2i + x))(-2i + x) = 0
((2i * 1 + x * 1) + -2x * (2i + x) + x2(2i + x))(-2i + x) = 0
((2i + 1x) + -2x * (2i + x) + x2(2i + x))(-2i + x) = 0
(2i + 1x + (2i * -2x + x * -2x) + x2(2i + x))(-2i + x) = 0
(2i + 1x + (-4ix + -2x2) + x2(2i + x))(-2i + x) = 0
(2i + 1x + -4ix + -2x2 + (2i * x2 + x * x2))(-2i + x) = 0
(2i + 1x + -4ix + -2x2 + (2ix2 + x3))(-2i + x) = 0

Reorder the terms:
(2i + -4ix + 2ix2 + 1x + -2x2 + x3)(-2i + x) = 0
(2i + -4ix + 2ix2 + 1x + -2x2 + x3)(-2i + x) = 0

Multiply (2i + -4ix + 2ix2 + 1x + -2x2 + x3) * (-2i + x)
(2i * (-2i + x) + -4ix * (-2i + x) + 2ix2 * (-2i + x) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
((-2i * 2i + x * 2i) + -4ix * (-2i + x) + 2ix2 * (-2i + x) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0

Reorder the terms:
((2ix + -4i2) + -4ix * (-2i + x) + 2ix2 * (-2i + x) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
((2ix + -4i2) + -4ix * (-2i + x) + 2ix2 * (-2i + x) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
(2ix + -4i2 + (-2i * -4ix + x * -4ix) + 2ix2 * (-2i + x) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0

Reorder the terms:
(2ix + -4i2 + (-4ix2 + 8i2x) + 2ix2 * (-2i + x) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
(2ix + -4i2 + (-4ix2 + 8i2x) + 2ix2 * (-2i + x) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
(2ix + -4i2 + -4ix2 + 8i2x + (-2i * 2ix2 + x * 2ix2) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0

Reorder the terms:
(2ix + -4i2 + -4ix2 + 8i2x + (2ix3 + -4i2x2) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
(2ix + -4i2 + -4ix2 + 8i2x + (2ix3 + -4i2x2) + 1x * (-2i + x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
(2ix + -4i2 + -4ix2 + 8i2x + 2ix3 + -4i2x2 + (-2i * 1x + x * 1x) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
(2ix + -4i2 + -4ix2 + 8i2x + 2ix3 + -4i2x2 + (-2ix + 1x2) + -2x2 * (-2i + x) + x3(-2i + x)) = 0
(2ix + -4i2 + -4ix2 + 8i2x + 2ix3 + -4i2x2 + -2ix + 1x2 + (-2i * -2x2 + x * -2x2) + x3(-2i + x)) = 0
(2ix + -4i2 + -4ix2 + 8i2x + 2ix3 + -4i2x2 + -2ix + 1x2 + (4ix2 + -2x3) + x3(-2i + x)) = 0
(2ix + -4i2 + -4ix2 + 8i2x + 2ix3 + -4i2x2 + -2ix + 1x2 + 4ix2 + -2x3 + (-2i * x3 + x * x3)) = 0
(2ix + -4i2 + -4ix2 + 8i2x + 2ix3 + -4i2x2 + -2ix + 1x2 + 4ix2 + -2x3 + (-2ix3 + x4)) = 0

Reorder the terms:
(2ix + -2ix + -4ix2 + 4ix2 + 2ix3 + -2ix3 + -4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + x4) = 0

Combine like terms: 2ix + -2ix = 0
(0 + -4ix2 + 4ix2 + 2ix3 + -2ix3 + -4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + x4) = 0
(-4ix2 + 4ix2 + 2ix3 + -2ix3 + -4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + x4) = 0

Combine like terms: -4ix2 + 4ix2 = 0
(0 + 2ix3 + -2ix3 + -4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + x4) = 0
(2ix3 + -2ix3 + -4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + x4) = 0

Combine like terms: 2ix3 + -2ix3 = 0
(0 + -4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + x4) = 0
(-4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + x4) = 0

Solving
-4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + x4 = 0

Solving for variable 'i'.

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

Add '-1x2' to each side of the equation.
-4i2 + 8i2x + -4i2x2 + 1x2 + -2x3 + -1x2 + x4 = 0 + -1x2

Reorder the terms:
-4i2 + 8i2x + -4i2x2 + 1x2 + -1x2 + -2x3 + x4 = 0 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-4i2 + 8i2x + -4i2x2 + 0 + -2x3 + x4 = 0 + -1x2
-4i2 + 8i2x + -4i2x2 + -2x3 + x4 = 0 + -1x2
Remove the zero:
-4i2 + 8i2x + -4i2x2 + -2x3 + x4 = -1x2

Add '2x3' to each side of the equation.
-4i2 + 8i2x + -4i2x2 + -2x3 + 2x3 + x4 = -1x2 + 2x3

Combine like terms: -2x3 + 2x3 = 0
-4i2 + 8i2x + -4i2x2 + 0 + x4 = -1x2 + 2x3
-4i2 + 8i2x + -4i2x2 + x4 = -1x2 + 2x3

Add '-1x4' to each side of the equation.
-4i2 + 8i2x + -4i2x2 + x4 + -1x4 = -1x2 + 2x3 + -1x4

Combine like terms: x4 + -1x4 = 0
-4i2 + 8i2x + -4i2x2 + 0 = -1x2 + 2x3 + -1x4
-4i2 + 8i2x + -4i2x2 = -1x2 + 2x3 + -1x4

Reorder the terms:
-4i2 + 8i2x + -4i2x2 + x2 + -2x3 + x4 = -1x2 + x2 + 2x3 + -2x3 + -1x4 + x4

Combine like terms: -1x2 + x2 = 0
-4i2 + 8i2x + -4i2x2 + x2 + -2x3 + x4 = 0 + 2x3 + -2x3 + -1x4 + x4
-4i2 + 8i2x + -4i2x2 + x2 + -2x3 + x4 = 2x3 + -2x3 + -1x4 + x4

Combine like terms: 2x3 + -2x3 = 0
-4i2 + 8i2x + -4i2x2 + x2 + -2x3 + x4 = 0 + -1x4 + x4
-4i2 + 8i2x + -4i2x2 + x2 + -2x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
-4i2 + 8i2x + -4i2x2 + x2 + -2x3 + x4 = 0

The solution to this equation could not be determined.

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