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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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