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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Combine like terms: -2x + -1x = -3x
(2 + -8i2 + -4i2x + -3x + 1x2 + -1x2 + x3) = 0

Combine like terms: 1x2 + -1x2 = 0
(2 + -8i2 + -4i2x + -3x + 0 + x3) = 0
(2 + -8i2 + -4i2x + -3x + x3) = 0

Solving
2 + -8i2 + -4i2x + -3x + x3 = 0

Solving for variable 'i'.

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

Add '-2' to each side of the equation.
2 + -8i2 + -4i2x + -3x + -2 + x3 = 0 + -2

Reorder the terms:
2 + -2 + -8i2 + -4i2x + -3x + x3 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -8i2 + -4i2x + -3x + x3 = 0 + -2
-8i2 + -4i2x + -3x + x3 = 0 + -2

Combine like terms: 0 + -2 = -2
-8i2 + -4i2x + -3x + x3 = -2

Add '3x' to each side of the equation.
-8i2 + -4i2x + -3x + 3x + x3 = -2 + 3x

Combine like terms: -3x + 3x = 0
-8i2 + -4i2x + 0 + x3 = -2 + 3x
-8i2 + -4i2x + x3 = -2 + 3x

Add '-1x3' to each side of the equation.
-8i2 + -4i2x + x3 + -1x3 = -2 + 3x + -1x3

Combine like terms: x3 + -1x3 = 0
-8i2 + -4i2x + 0 = -2 + 3x + -1x3
-8i2 + -4i2x = -2 + 3x + -1x3

Reorder the terms:
2 + -8i2 + -4i2x + -3x + x3 = -2 + 3x + -1x3 + 2 + -3x + x3

Reorder the terms:
2 + -8i2 + -4i2x + -3x + x3 = -2 + 2 + 3x + -3x + -1x3 + x3

Combine like terms: -2 + 2 = 0
2 + -8i2 + -4i2x + -3x + x3 = 0 + 3x + -3x + -1x3 + x3
2 + -8i2 + -4i2x + -3x + x3 = 3x + -3x + -1x3 + x3

Combine like terms: 3x + -3x = 0
2 + -8i2 + -4i2x + -3x + x3 = 0 + -1x3 + x3
2 + -8i2 + -4i2x + -3x + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
2 + -8i2 + -4i2x + -3x + x3 = 0

The solution to this equation could not be determined.

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