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

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


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

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

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

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

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

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

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

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

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

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

Solving
36 + -4i2 + 12x + x2 = 0

Solving for variable 'i'.

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

Add '-36' to each side of the equation.
36 + -4i2 + 12x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -4i2 + 12x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -4i2 + 12x + x2 = 0 + -36
-4i2 + 12x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-4i2 + 12x + x2 = -36

Add '-12x' to each side of the equation.
-4i2 + 12x + -12x + x2 = -36 + -12x

Combine like terms: 12x + -12x = 0
-4i2 + 0 + x2 = -36 + -12x
-4i2 + x2 = -36 + -12x

Add '-1x2' to each side of the equation.
-4i2 + x2 + -1x2 = -36 + -12x + -1x2

Combine like terms: x2 + -1x2 = 0
-4i2 + 0 = -36 + -12x + -1x2
-4i2 = -36 + -12x + -1x2

Divide each side by '-4'.
i2 = 9 + 3x + 0.25x2

Simplifying
i2 = 9 + 3x + 0.25x2

Reorder the terms:
-9 + i2 + -3x + -0.25x2 = 9 + 3x + 0.25x2 + -9 + -3x + -0.25x2

Reorder the terms:
-9 + i2 + -3x + -0.25x2 = 9 + -9 + 3x + -3x + 0.25x2 + -0.25x2

Combine like terms: 9 + -9 = 0
-9 + i2 + -3x + -0.25x2 = 0 + 3x + -3x + 0.25x2 + -0.25x2
-9 + i2 + -3x + -0.25x2 = 3x + -3x + 0.25x2 + -0.25x2

Combine like terms: 3x + -3x = 0
-9 + i2 + -3x + -0.25x2 = 0 + 0.25x2 + -0.25x2
-9 + i2 + -3x + -0.25x2 = 0.25x2 + -0.25x2

Combine like terms: 0.25x2 + -0.25x2 = 0.00
-9 + i2 + -3x + -0.25x2 = 0.00

The solution to this equation could not be determined.

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