(x-6+2i)(x-6-2i)(x+3)=0

Solution for (x-6+2i)(x-6-2i)(x+3)=0 equation:

Simplifying
(x + -6 + 2i)(x + -6 + -2i)(x + 3) = 0

Reorder the terms:
(-6 + 2i + x)(x + -6 + -2i)(x + 3) = 0

Reorder the terms:
(-6 + 2i + x)(-6 + -2i + x)(x + 3) = 0

Reorder the terms:
(-6 + 2i + x)(-6 + -2i + x)(3 + x) = 0

Multiply (-6 + 2i + x) * (-6 + -2i + x)
(-6(-6 + -2i + x) + 2i * (-6 + -2i + x) + x(-6 + -2i + x))(3 + x) = 0
((-6 * -6 + -2i * -6 + x * -6) + 2i * (-6 + -2i + x) + x(-6 + -2i + x))(3 + x) = 0
((36 + 12i + -6x) + 2i * (-6 + -2i + x) + x(-6 + -2i + x))(3 + x) = 0
(36 + 12i + -6x + (-6 * 2i + -2i * 2i + x * 2i) + x(-6 + -2i + x))(3 + x) = 0

Reorder the terms:
(36 + 12i + -6x + (-12i + 2ix + -4i2) + x(-6 + -2i + x))(3 + x) = 0
(36 + 12i + -6x + (-12i + 2ix + -4i2) + x(-6 + -2i + x))(3 + x) = 0
(36 + 12i + -6x + -12i + 2ix + -4i2 + (-6 * x + -2i * x + x * x))(3 + x) = 0

Reorder the terms:
(36 + 12i + -6x + -12i + 2ix + -4i2 + (-2ix + -6x + x2))(3 + x) = 0
(36 + 12i + -6x + -12i + 2ix + -4i2 + (-2ix + -6x + x2))(3 + x) = 0

Reorder the terms:
(36 + 12i + -12i + 2ix + -2ix + -4i2 + -6x + -6x + x2)(3 + x) = 0

Combine like terms: 12i + -12i = 0
(36 + 0 + 2ix + -2ix + -4i2 + -6x + -6x + x2)(3 + x) = 0
(36 + 2ix + -2ix + -4i2 + -6x + -6x + x2)(3 + x) = 0

Combine like terms: 2ix + -2ix = 0
(36 + 0 + -4i2 + -6x + -6x + x2)(3 + x) = 0
(36 + -4i2 + -6x + -6x + x2)(3 + x) = 0

Combine like terms: -6x + -6x = -12x
(36 + -4i2 + -12x + x2)(3 + x) = 0

Multiply (36 + -4i2 + -12x + x2) * (3 + x)
(36(3 + x) + -4i2 * (3 + x) + -12x * (3 + x) + x2(3 + x)) = 0
((3 * 36 + x * 36) + -4i2 * (3 + x) + -12x * (3 + x) + x2(3 + x)) = 0
((108 + 36x) + -4i2 * (3 + x) + -12x * (3 + x) + x2(3 + x)) = 0
(108 + 36x + (3 * -4i2 + x * -4i2) + -12x * (3 + x) + x2(3 + x)) = 0
(108 + 36x + (-12i2 + -4i2x) + -12x * (3 + x) + x2(3 + x)) = 0
(108 + 36x + -12i2 + -4i2x + (3 * -12x + x * -12x) + x2(3 + x)) = 0
(108 + 36x + -12i2 + -4i2x + (-36x + -12x2) + x2(3 + x)) = 0
(108 + 36x + -12i2 + -4i2x + -36x + -12x2 + (3 * x2 + x * x2)) = 0
(108 + 36x + -12i2 + -4i2x + -36x + -12x2 + (3x2 + x3)) = 0

Reorder the terms:
(108 + -12i2 + -4i2x + 36x + -36x + -12x2 + 3x2 + x3) = 0

Combine like terms: 36x + -36x = 0
(108 + -12i2 + -4i2x + 0 + -12x2 + 3x2 + x3) = 0
(108 + -12i2 + -4i2x + -12x2 + 3x2 + x3) = 0

Combine like terms: -12x2 + 3x2 = -9x2
(108 + -12i2 + -4i2x + -9x2 + x3) = 0

Solving
108 + -12i2 + -4i2x + -9x2 + x3 = 0

Solving for variable 'i'.

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

Add '-108' to each side of the equation.
108 + -12i2 + -4i2x + -9x2 + -108 + x3 = 0 + -108

Reorder the terms:
108 + -108 + -12i2 + -4i2x + -9x2 + x3 = 0 + -108

Combine like terms: 108 + -108 = 0
0 + -12i2 + -4i2x + -9x2 + x3 = 0 + -108
-12i2 + -4i2x + -9x2 + x3 = 0 + -108

Combine like terms: 0 + -108 = -108
-12i2 + -4i2x + -9x2 + x3 = -108

Add '9x2' to each side of the equation.
-12i2 + -4i2x + -9x2 + 9x2 + x3 = -108 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-12i2 + -4i2x + 0 + x3 = -108 + 9x2
-12i2 + -4i2x + x3 = -108 + 9x2

Add '-1x3' to each side of the equation.
-12i2 + -4i2x + x3 + -1x3 = -108 + 9x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-12i2 + -4i2x + 0 = -108 + 9x2 + -1x3
-12i2 + -4i2x = -108 + 9x2 + -1x3

Reorder the terms:
108 + -12i2 + -4i2x + -9x2 + x3 = -108 + 9x2 + -1x3 + 108 + -9x2 + x3

Reorder the terms:
108 + -12i2 + -4i2x + -9x2 + x3 = -108 + 108 + 9x2 + -9x2 + -1x3 + x3

Combine like terms: -108 + 108 = 0
108 + -12i2 + -4i2x + -9x2 + x3 = 0 + 9x2 + -9x2 + -1x3 + x3
108 + -12i2 + -4i2x + -9x2 + x3 = 9x2 + -9x2 + -1x3 + x3

Combine like terms: 9x2 + -9x2 = 0
108 + -12i2 + -4i2x + -9x2 + x3 = 0 + -1x3 + x3
108 + -12i2 + -4i2x + -9x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
108 + -12i2 + -4i2x + -9x2 + x3 = 0

The solution to this equation could not be determined.