(x+1)[x-(3-4i)][x-(3+4i)]=0

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Solution for (x+1)[x-(3-4i)][x-(3+4i)]=0 equation:


Simplifying
(x + 1)[x + -1(3 + -4i)][x + -1(3 + 4i)] = 0

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

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

Reorder the terms:
(1 + x)[-3 + 4i + x][-3 + -4i + x] = 0

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

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

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

Combine like terms: 1x + -3x = -2x
(-3 + 4i + 4ix + -2x + x2)[-3 + -4i + x] = 0

Multiply (-3 + 4i + 4ix + -2x + x2) * [-3 + -4i + x]
(-3[-3 + -4i + x] + 4i * [-3 + -4i + x] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0
([-3 * -3 + -4i * -3 + x * -3] + 4i * [-3 + -4i + x] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0
([9 + 12i + -3x] + 4i * [-3 + -4i + x] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0
(9 + 12i + -3x + [-3 * 4i + -4i * 4i + x * 4i] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0

Reorder the terms:
(9 + 12i + -3x + [-12i + 4ix + -16i2] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0
(9 + 12i + -3x + [-12i + 4ix + -16i2] + 4ix * [-3 + -4i + x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0
(9 + 12i + -3x + -12i + 4ix + -16i2 + [-3 * 4ix + -4i * 4ix + x * 4ix] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0

Reorder the terms:
(9 + 12i + -3x + -12i + 4ix + -16i2 + [-12ix + 4ix2 + -16i2x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0
(9 + 12i + -3x + -12i + 4ix + -16i2 + [-12ix + 4ix2 + -16i2x] + -2x * [-3 + -4i + x] + x2[-3 + -4i + x]) = 0
(9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + [-3 * -2x + -4i * -2x + x * -2x] + x2[-3 + -4i + x]) = 0

Reorder the terms:
(9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + [8ix + 6x + -2x2] + x2[-3 + -4i + x]) = 0
(9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + [8ix + 6x + -2x2] + x2[-3 + -4i + x]) = 0
(9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + 8ix + 6x + -2x2 + [-3 * x2 + -4i * x2 + x * x2]) = 0

Reorder the terms:
(9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + 8ix + 6x + -2x2 + [-4ix2 + -3x2 + x3]) = 0
(9 + 12i + -3x + -12i + 4ix + -16i2 + -12ix + 4ix2 + -16i2x + 8ix + 6x + -2x2 + [-4ix2 + -3x2 + x3]) = 0

Reorder the terms:
(9 + 12i + -12i + 4ix + -12ix + 8ix + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0

Combine like terms: 12i + -12i = 0
(9 + 0 + 4ix + -12ix + 8ix + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0
(9 + 4ix + -12ix + 8ix + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0

Combine like terms: 4ix + -12ix = -8ix
(9 + -8ix + 8ix + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0

Combine like terms: -8ix + 8ix = 0
(9 + 0 + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0
(9 + 4ix2 + -4ix2 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0

Combine like terms: 4ix2 + -4ix2 = 0
(9 + 0 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0
(9 + -16i2 + -16i2x + -3x + 6x + -2x2 + -3x2 + x3) = 0

Combine like terms: -3x + 6x = 3x
(9 + -16i2 + -16i2x + 3x + -2x2 + -3x2 + x3) = 0

Combine like terms: -2x2 + -3x2 = -5x2
(9 + -16i2 + -16i2x + 3x + -5x2 + x3) = 0

Solving
9 + -16i2 + -16i2x + 3x + -5x2 + 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 + -16i2 + -16i2x + 3x + -5x2 + -9 + x3 = 0 + -9

Reorder the terms:
9 + -9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -9
-16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -9

Combine like terms: 0 + -9 = -9
-16i2 + -16i2x + 3x + -5x2 + x3 = -9

Add '-3x' to each side of the equation.
-16i2 + -16i2x + 3x + -5x2 + -3x + x3 = -9 + -3x

Reorder the terms:
-16i2 + -16i2x + 3x + -3x + -5x2 + x3 = -9 + -3x

Combine like terms: 3x + -3x = 0
-16i2 + -16i2x + 0 + -5x2 + x3 = -9 + -3x
-16i2 + -16i2x + -5x2 + x3 = -9 + -3x

Add '5x2' to each side of the equation.
-16i2 + -16i2x + -5x2 + 5x2 + x3 = -9 + -3x + 5x2

Combine like terms: -5x2 + 5x2 = 0
-16i2 + -16i2x + 0 + x3 = -9 + -3x + 5x2
-16i2 + -16i2x + x3 = -9 + -3x + 5x2

Add '-1x3' to each side of the equation.
-16i2 + -16i2x + x3 + -1x3 = -9 + -3x + 5x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-16i2 + -16i2x + 0 = -9 + -3x + 5x2 + -1x3
-16i2 + -16i2x = -9 + -3x + 5x2 + -1x3

Reorder the terms:
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = -9 + -3x + 5x2 + -1x3 + 9 + 3x + -5x2 + x3

Reorder the terms:
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = -9 + 9 + -3x + 3x + 5x2 + -5x2 + -1x3 + x3

Combine like terms: -9 + 9 = 0
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -3x + 3x + 5x2 + -5x2 + -1x3 + x3
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = -3x + 3x + 5x2 + -5x2 + -1x3 + x3

Combine like terms: -3x + 3x = 0
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + 5x2 + -5x2 + -1x3 + x3
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3

Combine like terms: 5x2 + -5x2 = 0
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0 + -1x3 + x3
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
9 + -16i2 + -16i2x + 3x + -5x2 + x3 = 0

The solution to this equation could not be determined.

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