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

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


Simplifying
(x + -1(3x + -2i))(x + -1(3x + 2i)) = 0

Reorder the terms:
(x + -1(-2i + 3x))(x + -1(3x + 2i)) = 0
(x + (-2i * -1 + 3x * -1))(x + -1(3x + 2i)) = 0
(x + (2i + -3x))(x + -1(3x + 2i)) = 0

Reorder the terms:
(2i + x + -3x)(x + -1(3x + 2i)) = 0

Combine like terms: x + -3x = -2x
(2i + -2x)(x + -1(3x + 2i)) = 0

Reorder the terms:
(2i + -2x)(x + -1(2i + 3x)) = 0
(2i + -2x)(x + (2i * -1 + 3x * -1)) = 0
(2i + -2x)(x + (-2i + -3x)) = 0

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

Combine like terms: x + -3x = -2x
(2i + -2x)(-2i + -2x) = 0

Multiply (2i + -2x) * (-2i + -2x)
(2i * (-2i + -2x) + -2x * (-2i + -2x)) = 0
((-2i * 2i + -2x * 2i) + -2x * (-2i + -2x)) = 0

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

Reorder the terms:
(-4ix + 4ix + -4i2 + 4x2) = 0

Combine like terms: -4ix + 4ix = 0
(0 + -4i2 + 4x2) = 0
(-4i2 + 4x2) = 0

Solving
-4i2 + 4x2 = 0

Solving for variable 'i'.

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

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

Combine like terms: 4x2 + -4x2 = 0
-4i2 + 0 = 0 + -4x2
-4i2 = 0 + -4x2
Remove the zero:
-4i2 = -4x2

Divide each side by '-4'.
i2 = x2

Simplifying
i2 = x2

Take the square root of each side:
i = {-1x, x}

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