(x+6)[x-(5-2i)][x-(5+2i)]=0

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Solution for (x+6)[x-(5-2i)][x-(5+2i)]=0 equation: 


Simplifying
(x + 6)[x + -1(5 + -2i)][x + -1(5 + 2i)] = 0

Reorder the terms:
(6 + x)[x + -1(5 + -2i)][x + -1(5 + 2i)] = 0
(6 + x)[x + (5 * -1 + -2i * -1)][x + -1(5 + 2i)] = 0
(6 + x)[x + (-5 + 2i)][x + -1(5 + 2i)] = 0

Reorder the terms:
(6 + x)[-5 + 2i + x][x + -1(5 + 2i)] = 0
(6 + x)[-5 + 2i + x][x + (5 * -1 + 2i * -1)] = 0
(6 + x)[-5 + 2i + x][x + (-5 + -2i)] = 0

Reorder the terms:
(6 + x)[-5 + 2i + x][-5 + -2i + x] = 0

Multiply (6 + x) * [-5 + 2i + x]
(6[-5 + 2i + x] + x[-5 + 2i + x])[-5 + -2i + x] = 0
([-5 * 6 + 2i * 6 + x * 6] + x[-5 + 2i + x])[-5 + -2i + x] = 0
([-30 + 12i + 6x] + x[-5 + 2i + x])[-5 + -2i + x] = 0
(-30 + 12i + 6x + [-5 * x + 2i * x + x * x])[-5 + -2i + x] = 0

Reorder the terms:
(-30 + 12i + 6x + [2ix + -5x + x2])[-5 + -2i + x] = 0
(-30 + 12i + 6x + [2ix + -5x + x2])[-5 + -2i + x] = 0

Reorder the terms:
(-30 + 12i + 2ix + 6x + -5x + x2)[-5 + -2i + x] = 0

Combine like terms: 6x + -5x = 1x
(-30 + 12i + 2ix + 1x + x2)[-5 + -2i + x] = 0

Multiply (-30 + 12i + 2ix + 1x + x2) * [-5 + -2i + x]
(-30[-5 + -2i + x] + 12i * [-5 + -2i + x] + 2ix * [-5 + -2i + x] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0
([-5 * -30 + -2i * -30 + x * -30] + 12i * [-5 + -2i + x] + 2ix * [-5 + -2i + x] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0
([150 + 60i + -30x] + 12i * [-5 + -2i + x] + 2ix * [-5 + -2i + x] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0
(150 + 60i + -30x + [-5 * 12i + -2i * 12i + x * 12i] + 2ix * [-5 + -2i + x] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0

Reorder the terms:
(150 + 60i + -30x + [-60i + 12ix + -24i2] + 2ix * [-5 + -2i + x] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0
(150 + 60i + -30x + [-60i + 12ix + -24i2] + 2ix * [-5 + -2i + x] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0
(150 + 60i + -30x + -60i + 12ix + -24i2 + [-5 * 2ix + -2i * 2ix + x * 2ix] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0

Reorder the terms:
(150 + 60i + -30x + -60i + 12ix + -24i2 + [-10ix + 2ix2 + -4i2x] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0
(150 + 60i + -30x + -60i + 12ix + -24i2 + [-10ix + 2ix2 + -4i2x] + 1x * [-5 + -2i + x] + x2[-5 + -2i + x]) = 0
(150 + 60i + -30x + -60i + 12ix + -24i2 + -10ix + 2ix2 + -4i2x + [-5 * 1x + -2i * 1x + x * 1x] + x2[-5 + -2i + x]) = 0

Reorder the terms:
(150 + 60i + -30x + -60i + 12ix + -24i2 + -10ix + 2ix2 + -4i2x + [-2ix + -5x + 1x2] + x2[-5 + -2i + x]) = 0
(150 + 60i + -30x + -60i + 12ix + -24i2 + -10ix + 2ix2 + -4i2x + [-2ix + -5x + 1x2] + x2[-5 + -2i + x]) = 0
(150 + 60i + -30x + -60i + 12ix + -24i2 + -10ix + 2ix2 + -4i2x + -2ix + -5x + 1x2 + [-5 * x2 + -2i * x2 + x * x2]) = 0

Reorder the terms:
(150 + 60i + -30x + -60i + 12ix + -24i2 + -10ix + 2ix2 + -4i2x + -2ix + -5x + 1x2 + [-2ix2 + -5x2 + x3]) = 0
(150 + 60i + -30x + -60i + 12ix + -24i2 + -10ix + 2ix2 + -4i2x + -2ix + -5x + 1x2 + [-2ix2 + -5x2 + x3]) = 0

Reorder the terms:
(150 + 60i + -60i + 12ix + -10ix + -2ix + 2ix2 + -2ix2 + -24i2 + -4i2x + -30x + -5x + 1x2 + -5x2 + x3) = 0

Combine like terms: 60i + -60i = 0
(150 + 0 + 12ix + -10ix + -2ix + 2ix2 + -2ix2 + -24i2 + -4i2x + -30x + -5x + 1x2 + -5x2 + x3) = 0
(150 + 12ix + -10ix + -2ix + 2ix2 + -2ix2 + -24i2 + -4i2x + -30x + -5x + 1x2 + -5x2 + x3) = 0

Combine like terms: 12ix + -10ix = 2ix
(150 + 2ix + -2ix + 2ix2 + -2ix2 + -24i2 + -4i2x + -30x + -5x + 1x2 + -5x2 + x3) = 0

Combine like terms: 2ix + -2ix = 0
(150 + 0 + 2ix2 + -2ix2 + -24i2 + -4i2x + -30x + -5x + 1x2 + -5x2 + x3) = 0
(150 + 2ix2 + -2ix2 + -24i2 + -4i2x + -30x + -5x + 1x2 + -5x2 + x3) = 0

Combine like terms: 2ix2 + -2ix2 = 0
(150 + 0 + -24i2 + -4i2x + -30x + -5x + 1x2 + -5x2 + x3) = 0
(150 + -24i2 + -4i2x + -30x + -5x + 1x2 + -5x2 + x3) = 0

Combine like terms: -30x + -5x = -35x
(150 + -24i2 + -4i2x + -35x + 1x2 + -5x2 + x3) = 0

Combine like terms: 1x2 + -5x2 = -4x2
(150 + -24i2 + -4i2x + -35x + -4x2 + x3) = 0

Solving
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = 0

Solving for variable 'i'.

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

Add '-150' to each side of the equation.
150 + -24i2 + -4i2x + -35x + -4x2 + -150 + x3 = 0 + -150

Reorder the terms:
150 + -150 + -24i2 + -4i2x + -35x + -4x2 + x3 = 0 + -150

Combine like terms: 150 + -150 = 0
0 + -24i2 + -4i2x + -35x + -4x2 + x3 = 0 + -150
-24i2 + -4i2x + -35x + -4x2 + x3 = 0 + -150

Combine like terms: 0 + -150 = -150
-24i2 + -4i2x + -35x + -4x2 + x3 = -150

Add '35x' to each side of the equation.
-24i2 + -4i2x + -35x + -4x2 + 35x + x3 = -150 + 35x

Reorder the terms:
-24i2 + -4i2x + -35x + 35x + -4x2 + x3 = -150 + 35x

Combine like terms: -35x + 35x = 0
-24i2 + -4i2x + 0 + -4x2 + x3 = -150 + 35x
-24i2 + -4i2x + -4x2 + x3 = -150 + 35x

Add '4x2' to each side of the equation.
-24i2 + -4i2x + -4x2 + 4x2 + x3 = -150 + 35x + 4x2

Combine like terms: -4x2 + 4x2 = 0
-24i2 + -4i2x + 0 + x3 = -150 + 35x + 4x2
-24i2 + -4i2x + x3 = -150 + 35x + 4x2

Add '-1x3' to each side of the equation.
-24i2 + -4i2x + x3 + -1x3 = -150 + 35x + 4x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-24i2 + -4i2x + 0 = -150 + 35x + 4x2 + -1x3
-24i2 + -4i2x = -150 + 35x + 4x2 + -1x3

Reorder the terms:
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = -150 + 35x + 4x2 + -1x3 + 150 + -35x + -4x2 + x3

Reorder the terms:
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = -150 + 150 + 35x + -35x + 4x2 + -4x2 + -1x3 + x3

Combine like terms: -150 + 150 = 0
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = 0 + 35x + -35x + 4x2 + -4x2 + -1x3 + x3
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = 35x + -35x + 4x2 + -4x2 + -1x3 + x3

Combine like terms: 35x + -35x = 0
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = 0 + 4x2 + -4x2 + -1x3 + x3
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = 4x2 + -4x2 + -1x3 + x3

Combine like terms: 4x2 + -4x2 = 0
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = 0 + -1x3 + x3
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
150 + -24i2 + -4i2x + -35x + -4x2 + x3 = 0

The solution to this equation could not be determined.

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