(x+1)[x-(4-7i)][x-(4+7i)]=0

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Solution for (x+1)[x-(4-7i)][x-(4+7i)]=0 equation: 


Simplifying
(x + 1)[x + -1(4 + -7i)][x + -1(4 + 7i)] = 0

Reorder the terms:
(1 + x)[x + -1(4 + -7i)][x + -1(4 + 7i)] = 0
(1 + x)[x + (4 * -1 + -7i * -1)][x + -1(4 + 7i)] = 0
(1 + x)[x + (-4 + 7i)][x + -1(4 + 7i)] = 0

Reorder the terms:
(1 + x)[-4 + 7i + x][x + -1(4 + 7i)] = 0
(1 + x)[-4 + 7i + x][x + (4 * -1 + 7i * -1)] = 0
(1 + x)[-4 + 7i + x][x + (-4 + -7i)] = 0

Reorder the terms:
(1 + x)[-4 + 7i + x][-4 + -7i + x] = 0

Multiply (1 + x) * [-4 + 7i + x]
(1[-4 + 7i + x] + x[-4 + 7i + x])[-4 + -7i + x] = 0
([-4 * 1 + 7i * 1 + x * 1] + x[-4 + 7i + x])[-4 + -7i + x] = 0
([-4 + 7i + 1x] + x[-4 + 7i + x])[-4 + -7i + x] = 0
(-4 + 7i + 1x + [-4 * x + 7i * x + x * x])[-4 + -7i + x] = 0

Reorder the terms:
(-4 + 7i + 1x + [7ix + -4x + x2])[-4 + -7i + x] = 0
(-4 + 7i + 1x + [7ix + -4x + x2])[-4 + -7i + x] = 0

Reorder the terms:
(-4 + 7i + 7ix + 1x + -4x + x2)[-4 + -7i + x] = 0

Combine like terms: 1x + -4x = -3x
(-4 + 7i + 7ix + -3x + x2)[-4 + -7i + x] = 0

Multiply (-4 + 7i + 7ix + -3x + x2) * [-4 + -7i + x]
(-4[-4 + -7i + x] + 7i * [-4 + -7i + x] + 7ix * [-4 + -7i + x] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0
([-4 * -4 + -7i * -4 + x * -4] + 7i * [-4 + -7i + x] + 7ix * [-4 + -7i + x] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0
([16 + 28i + -4x] + 7i * [-4 + -7i + x] + 7ix * [-4 + -7i + x] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0
(16 + 28i + -4x + [-4 * 7i + -7i * 7i + x * 7i] + 7ix * [-4 + -7i + x] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0

Reorder the terms:
(16 + 28i + -4x + [-28i + 7ix + -49i2] + 7ix * [-4 + -7i + x] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0
(16 + 28i + -4x + [-28i + 7ix + -49i2] + 7ix * [-4 + -7i + x] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0
(16 + 28i + -4x + -28i + 7ix + -49i2 + [-4 * 7ix + -7i * 7ix + x * 7ix] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0

Reorder the terms:
(16 + 28i + -4x + -28i + 7ix + -49i2 + [-28ix + 7ix2 + -49i2x] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0
(16 + 28i + -4x + -28i + 7ix + -49i2 + [-28ix + 7ix2 + -49i2x] + -3x * [-4 + -7i + x] + x2[-4 + -7i + x]) = 0
(16 + 28i + -4x + -28i + 7ix + -49i2 + -28ix + 7ix2 + -49i2x + [-4 * -3x + -7i * -3x + x * -3x] + x2[-4 + -7i + x]) = 0

Reorder the terms:
(16 + 28i + -4x + -28i + 7ix + -49i2 + -28ix + 7ix2 + -49i2x + [21ix + 12x + -3x2] + x2[-4 + -7i + x]) = 0
(16 + 28i + -4x + -28i + 7ix + -49i2 + -28ix + 7ix2 + -49i2x + [21ix + 12x + -3x2] + x2[-4 + -7i + x]) = 0
(16 + 28i + -4x + -28i + 7ix + -49i2 + -28ix + 7ix2 + -49i2x + 21ix + 12x + -3x2 + [-4 * x2 + -7i * x2 + x * x2]) = 0

Reorder the terms:
(16 + 28i + -4x + -28i + 7ix + -49i2 + -28ix + 7ix2 + -49i2x + 21ix + 12x + -3x2 + [-7ix2 + -4x2 + x3]) = 0
(16 + 28i + -4x + -28i + 7ix + -49i2 + -28ix + 7ix2 + -49i2x + 21ix + 12x + -3x2 + [-7ix2 + -4x2 + x3]) = 0

Reorder the terms:
(16 + 28i + -28i + 7ix + -28ix + 21ix + 7ix2 + -7ix2 + -49i2 + -49i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0

Combine like terms: 28i + -28i = 0
(16 + 0 + 7ix + -28ix + 21ix + 7ix2 + -7ix2 + -49i2 + -49i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0
(16 + 7ix + -28ix + 21ix + 7ix2 + -7ix2 + -49i2 + -49i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0

Combine like terms: 7ix + -28ix = -21ix
(16 + -21ix + 21ix + 7ix2 + -7ix2 + -49i2 + -49i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0

Combine like terms: -21ix + 21ix = 0
(16 + 0 + 7ix2 + -7ix2 + -49i2 + -49i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0
(16 + 7ix2 + -7ix2 + -49i2 + -49i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0

Combine like terms: 7ix2 + -7ix2 = 0
(16 + 0 + -49i2 + -49i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0
(16 + -49i2 + -49i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0

Combine like terms: -4x + 12x = 8x
(16 + -49i2 + -49i2x + 8x + -3x2 + -4x2 + x3) = 0

Combine like terms: -3x2 + -4x2 = -7x2
(16 + -49i2 + -49i2x + 8x + -7x2 + x3) = 0

Solving
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = 0

Solving for variable 'i'.

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

Add '-16' to each side of the equation.
16 + -49i2 + -49i2x + 8x + -7x2 + -16 + x3 = 0 + -16

Reorder the terms:
16 + -16 + -49i2 + -49i2x + 8x + -7x2 + x3 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -49i2 + -49i2x + 8x + -7x2 + x3 = 0 + -16
-49i2 + -49i2x + 8x + -7x2 + x3 = 0 + -16

Combine like terms: 0 + -16 = -16
-49i2 + -49i2x + 8x + -7x2 + x3 = -16

Add '-8x' to each side of the equation.
-49i2 + -49i2x + 8x + -7x2 + -8x + x3 = -16 + -8x

Reorder the terms:
-49i2 + -49i2x + 8x + -8x + -7x2 + x3 = -16 + -8x

Combine like terms: 8x + -8x = 0
-49i2 + -49i2x + 0 + -7x2 + x3 = -16 + -8x
-49i2 + -49i2x + -7x2 + x3 = -16 + -8x

Add '7x2' to each side of the equation.
-49i2 + -49i2x + -7x2 + 7x2 + x3 = -16 + -8x + 7x2

Combine like terms: -7x2 + 7x2 = 0
-49i2 + -49i2x + 0 + x3 = -16 + -8x + 7x2
-49i2 + -49i2x + x3 = -16 + -8x + 7x2

Add '-1x3' to each side of the equation.
-49i2 + -49i2x + x3 + -1x3 = -16 + -8x + 7x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-49i2 + -49i2x + 0 = -16 + -8x + 7x2 + -1x3
-49i2 + -49i2x = -16 + -8x + 7x2 + -1x3

Reorder the terms:
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = -16 + -8x + 7x2 + -1x3 + 16 + 8x + -7x2 + x3

Reorder the terms:
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = -16 + 16 + -8x + 8x + 7x2 + -7x2 + -1x3 + x3

Combine like terms: -16 + 16 = 0
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = 0 + -8x + 8x + 7x2 + -7x2 + -1x3 + x3
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = -8x + 8x + 7x2 + -7x2 + -1x3 + x3

Combine like terms: -8x + 8x = 0
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = 0 + 7x2 + -7x2 + -1x3 + x3
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = 7x2 + -7x2 + -1x3 + x3

Combine like terms: 7x2 + -7x2 = 0
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = 0 + -1x3 + x3
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
16 + -49i2 + -49i2x + 8x + -7x2 + x3 = 0

The solution to this equation could not be determined.

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