(x-1)[x-(3+i)][x-(3-i)]=0

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Solution for (x-1)[x-(3+i)][x-(3-i)]=0 equation: 


Simplifying
(x + -1)[x + -1(3 + i)][x + -1(3 + -1i)] = 0

Reorder the terms:
(-1 + x)[x + -1(3 + i)][x + -1(3 + -1i)] = 0
(-1 + x)[x + (3 * -1 + i * -1)][x + -1(3 + -1i)] = 0
(-1 + x)[x + (-3 + -1i)][x + -1(3 + -1i)] = 0

Reorder the terms:
(-1 + x)[-3 + -1i + x][x + -1(3 + -1i)] = 0
(-1 + x)[-3 + -1i + x][x + (3 * -1 + -1i * -1)] = 0
(-1 + x)[-3 + -1i + x][x + (-3 + 1i)] = 0

Reorder the terms:
(-1 + x)[-3 + -1i + x][-3 + 1i + x] = 0

Multiply (-1 + x) * [-3 + -1i + x]
(-1[-3 + -1i + x] + x[-3 + -1i + x])[-3 + 1i + x] = 0
([-3 * -1 + -1i * -1 + x * -1] + x[-3 + -1i + x])[-3 + 1i + x] = 0
([3 + 1i + -1x] + x[-3 + -1i + x])[-3 + 1i + x] = 0
(3 + 1i + -1x + [-3 * x + -1i * x + x * x])[-3 + 1i + x] = 0

Reorder the terms:
(3 + 1i + -1x + [-1ix + -3x + x2])[-3 + 1i + x] = 0
(3 + 1i + -1x + [-1ix + -3x + x2])[-3 + 1i + x] = 0

Reorder the terms:
(3 + 1i + -1ix + -1x + -3x + x2)[-3 + 1i + x] = 0

Combine like terms: -1x + -3x = -4x
(3 + 1i + -1ix + -4x + x2)[-3 + 1i + x] = 0

Multiply (3 + 1i + -1ix + -4x + x2) * [-3 + 1i + x]
(3[-3 + 1i + x] + 1i * [-3 + 1i + x] + -1ix * [-3 + 1i + x] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0
([-3 * 3 + 1i * 3 + x * 3] + 1i * [-3 + 1i + x] + -1ix * [-3 + 1i + x] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0
([-9 + 3i + 3x] + 1i * [-3 + 1i + x] + -1ix * [-3 + 1i + x] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0
(-9 + 3i + 3x + [-3 * 1i + 1i * 1i + x * 1i] + -1ix * [-3 + 1i + x] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0

Reorder the terms:
(-9 + 3i + 3x + [-3i + 1ix + 1i2] + -1ix * [-3 + 1i + x] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0
(-9 + 3i + 3x + [-3i + 1ix + 1i2] + -1ix * [-3 + 1i + x] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0
(-9 + 3i + 3x + -3i + 1ix + 1i2 + [-3 * -1ix + 1i * -1ix + x * -1ix] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0

Reorder the terms:
(-9 + 3i + 3x + -3i + 1ix + 1i2 + [3ix + -1ix2 + -1i2x] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0
(-9 + 3i + 3x + -3i + 1ix + 1i2 + [3ix + -1ix2 + -1i2x] + -4x * [-3 + 1i + x] + x2[-3 + 1i + x]) = 0
(-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + [-3 * -4x + 1i * -4x + x * -4x] + x2[-3 + 1i + x]) = 0

Reorder the terms:
(-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + [-4ix + 12x + -4x2] + x2[-3 + 1i + x]) = 0
(-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + [-4ix + 12x + -4x2] + x2[-3 + 1i + x]) = 0
(-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + -4ix + 12x + -4x2 + [-3 * x2 + 1i * x2 + x * x2]) = 0

Reorder the terms:
(-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + -4ix + 12x + -4x2 + [1ix2 + -3x2 + x3]) = 0
(-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + -4ix + 12x + -4x2 + [1ix2 + -3x2 + x3]) = 0

Reorder the terms:
(-9 + 3i + -3i + 1ix + 3ix + -4ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0

Combine like terms: 3i + -3i = 0
(-9 + 0 + 1ix + 3ix + -4ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0
(-9 + 1ix + 3ix + -4ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0

Combine like terms: 1ix + 3ix = 4ix
(-9 + 4ix + -4ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0

Combine like terms: 4ix + -4ix = 0
(-9 + 0 + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0
(-9 + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0

Combine like terms: -1ix2 + 1ix2 = 0
(-9 + 0 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0
(-9 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3) = 0

Combine like terms: 3x + 12x = 15x
(-9 + 1i2 + -1i2x + 15x + -4x2 + -3x2 + x3) = 0

Combine like terms: -4x2 + -3x2 = -7x2
(-9 + 1i2 + -1i2x + 15x + -7x2 + x3) = 0

Solving
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0

Solving for variable 'i'.

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

Add '9' to each side of the equation.
-9 + 1i2 + -1i2x + 15x + -7x2 + 9 + x3 = 0 + 9

Reorder the terms:
-9 + 9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + 9
1i2 + -1i2x + 15x + -7x2 + x3 = 0 + 9

Combine like terms: 0 + 9 = 9
1i2 + -1i2x + 15x + -7x2 + x3 = 9

Add '-15x' to each side of the equation.
1i2 + -1i2x + 15x + -7x2 + -15x + x3 = 9 + -15x

Reorder the terms:
1i2 + -1i2x + 15x + -15x + -7x2 + x3 = 9 + -15x

Combine like terms: 15x + -15x = 0
1i2 + -1i2x + 0 + -7x2 + x3 = 9 + -15x
1i2 + -1i2x + -7x2 + x3 = 9 + -15x

Add '7x2' to each side of the equation.
1i2 + -1i2x + -7x2 + 7x2 + x3 = 9 + -15x + 7x2

Combine like terms: -7x2 + 7x2 = 0
1i2 + -1i2x + 0 + x3 = 9 + -15x + 7x2
1i2 + -1i2x + x3 = 9 + -15x + 7x2

Add '-1x3' to each side of the equation.
1i2 + -1i2x + x3 + -1x3 = 9 + -15x + 7x2 + -1x3

Combine like terms: x3 + -1x3 = 0
1i2 + -1i2x + 0 = 9 + -15x + 7x2 + -1x3
1i2 + -1i2x = 9 + -15x + 7x2 + -1x3

Reorder the terms:
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 9 + -15x + 7x2 + -1x3 + -9 + 15x + -7x2 + x3

Reorder the terms:
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 9 + -9 + -15x + 15x + 7x2 + -7x2 + -1x3 + x3

Combine like terms: 9 + -9 = 0
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + -15x + 15x + 7x2 + -7x2 + -1x3 + x3
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = -15x + 15x + 7x2 + -7x2 + -1x3 + x3

Combine like terms: -15x + 15x = 0
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + 7x2 + -7x2 + -1x3 + x3
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 7x2 + -7x2 + -1x3 + x3

Combine like terms: 7x2 + -7x2 = 0
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0 + -1x3 + x3
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-9 + 1i2 + -1i2x + 15x + -7x2 + x3 = 0

The solution to this equation could not be determined.

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