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

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


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

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

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

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

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

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

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

Combine like terms: -1x + -2x = -3x
(2 + 1i + -1ix + -3x + x2)(-2 + 1i + x) = 0

Multiply (2 + 1i + -1ix + -3x + x2) * (-2 + 1i + x)
(2(-2 + 1i + x) + 1i * (-2 + 1i + x) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0
((-2 * 2 + 1i * 2 + x * 2) + 1i * (-2 + 1i + x) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0
((-4 + 2i + 2x) + 1i * (-2 + 1i + x) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0
(-4 + 2i + 2x + (-2 * 1i + 1i * 1i + x * 1i) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0

Reorder the terms:
(-4 + 2i + 2x + (-2i + 1ix + 1i2) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0
(-4 + 2i + 2x + (-2i + 1ix + 1i2) + -1ix * (-2 + 1i + x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0
(-4 + 2i + 2x + -2i + 1ix + 1i2 + (-2 * -1ix + 1i * -1ix + x * -1ix) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0

Reorder the terms:
(-4 + 2i + 2x + -2i + 1ix + 1i2 + (2ix + -1ix2 + -1i2x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0
(-4 + 2i + 2x + -2i + 1ix + 1i2 + (2ix + -1ix2 + -1i2x) + -3x * (-2 + 1i + x) + x2(-2 + 1i + x)) = 0
(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-2 * -3x + 1i * -3x + x * -3x) + x2(-2 + 1i + x)) = 0

Reorder the terms:
(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-3ix + 6x + -3x2) + x2(-2 + 1i + x)) = 0
(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + (-3ix + 6x + -3x2) + x2(-2 + 1i + x)) = 0
(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (-2 * x2 + 1i * x2 + x * x2)) = 0

Reorder the terms:
(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (1ix2 + -2x2 + x3)) = 0
(-4 + 2i + 2x + -2i + 1ix + 1i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + (1ix2 + -2x2 + x3)) = 0

Reorder the terms:
(-4 + 2i + -2i + 1ix + 2ix + -3ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0

Combine like terms: 2i + -2i = 0
(-4 + 0 + 1ix + 2ix + -3ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0
(-4 + 1ix + 2ix + -3ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0

Combine like terms: 1ix + 2ix = 3ix
(-4 + 3ix + -3ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0

Combine like terms: 3ix + -3ix = 0
(-4 + 0 + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0
(-4 + -1ix2 + 1ix2 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0

Combine like terms: -1ix2 + 1ix2 = 0
(-4 + 0 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0
(-4 + 1i2 + -1i2x + 2x + 6x + -3x2 + -2x2 + x3) = 0

Combine like terms: 2x + 6x = 8x
(-4 + 1i2 + -1i2x + 8x + -3x2 + -2x2 + x3) = 0

Combine like terms: -3x2 + -2x2 = -5x2
(-4 + 1i2 + -1i2x + 8x + -5x2 + x3) = 0

Solving
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 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 + -1i2x + 8x + -5x2 + 4 + x3 = 0 + 4

Reorder the terms:
-4 + 4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4
1i2 + -1i2x + 8x + -5x2 + x3 = 0 + 4

Combine like terms: 0 + 4 = 4
1i2 + -1i2x + 8x + -5x2 + x3 = 4

Add '-8x' to each side of the equation.
1i2 + -1i2x + 8x + -5x2 + -8x + x3 = 4 + -8x

Reorder the terms:
1i2 + -1i2x + 8x + -8x + -5x2 + x3 = 4 + -8x

Combine like terms: 8x + -8x = 0
1i2 + -1i2x + 0 + -5x2 + x3 = 4 + -8x
1i2 + -1i2x + -5x2 + x3 = 4 + -8x

Add '5x2' to each side of the equation.
1i2 + -1i2x + -5x2 + 5x2 + x3 = 4 + -8x + 5x2

Combine like terms: -5x2 + 5x2 = 0
1i2 + -1i2x + 0 + x3 = 4 + -8x + 5x2
1i2 + -1i2x + x3 = 4 + -8x + 5x2

Add '-1x3' to each side of the equation.
1i2 + -1i2x + x3 + -1x3 = 4 + -8x + 5x2 + -1x3

Combine like terms: x3 + -1x3 = 0
1i2 + -1i2x + 0 = 4 + -8x + 5x2 + -1x3
1i2 + -1i2x = 4 + -8x + 5x2 + -1x3

Reorder the terms:
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 4 + -8x + 5x2 + -1x3 + -4 + 8x + -5x2 + x3

Reorder the terms:
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 4 + -4 + -8x + 8x + 5x2 + -5x2 + -1x3 + x3

Combine like terms: 4 + -4 = 0
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + -8x + 8x + 5x2 + -5x2 + -1x3 + x3
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = -8x + 8x + 5x2 + -5x2 + -1x3 + x3

Combine like terms: -8x + 8x = 0
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + 5x2 + -5x2 + -1x3 + x3
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3

Combine like terms: 5x2 + -5x2 = 0
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0 + -1x3 + x3
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-4 + 1i2 + -1i2x + 8x + -5x2 + x3 = 0

The solution to this equation could not be determined.

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