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

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


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

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

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

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

Multiply (3 + x) * (2i + x)
(3(2i + x) + x(2i + x))(-2i + x) = 0
((2i * 3 + x * 3) + x(2i + x))(-2i + x) = 0
((6i + 3x) + x(2i + x))(-2i + x) = 0
(6i + 3x + (2i * x + x * x))(-2i + x) = 0
(6i + 3x + (2ix + x2))(-2i + x) = 0

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

Multiply (6i + 2ix + 3x + x2) * (-2i + x)
(6i * (-2i + x) + 2ix * (-2i + x) + 3x * (-2i + x) + x2(-2i + x)) = 0
((-2i * 6i + x * 6i) + 2ix * (-2i + x) + 3x * (-2i + x) + x2(-2i + x)) = 0

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

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

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

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

Combine like terms: 2ix2 + -2ix2 = 0
(0 + -12i2 + -4i2x + 3x2 + x3) = 0
(-12i2 + -4i2x + 3x2 + x3) = 0

Solving
-12i2 + -4i2x + 3x2 + x3 = 0

Solving for variable 'i'.

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

Add '-3x2' to each side of the equation.
-12i2 + -4i2x + 3x2 + -3x2 + x3 = 0 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12i2 + -4i2x + 0 + x3 = 0 + -3x2
-12i2 + -4i2x + x3 = 0 + -3x2
Remove the zero:
-12i2 + -4i2x + x3 = -3x2

Add '-1x3' to each side of the equation.
-12i2 + -4i2x + x3 + -1x3 = -3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-12i2 + -4i2x + 0 = -3x2 + -1x3
-12i2 + -4i2x = -3x2 + -1x3

Reorder the terms:
-12i2 + -4i2x + 3x2 + x3 = -3x2 + 3x2 + -1x3 + x3

Combine like terms: -3x2 + 3x2 = 0
-12i2 + -4i2x + 3x2 + x3 = 0 + -1x3 + x3
-12i2 + -4i2x + 3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-12i2 + -4i2x + 3x2 + x3 = 0

The solution to this equation could not be determined.

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