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

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


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

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

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

Multiply (-2i + -1x) * (2i + x)
(-2i * (2i + x) + -1x * (2i + x)) = 0
((2i * -2i + x * -2i) + -1x * (2i + x)) = 0

Reorder the terms:
((-2ix + -4i2) + -1x * (2i + x)) = 0
((-2ix + -4i2) + -1x * (2i + x)) = 0
(-2ix + -4i2 + (2i * -1x + x * -1x)) = 0
(-2ix + -4i2 + (-2ix + -1x2)) = 0

Reorder the terms:
(-2ix + -2ix + -4i2 + -1x2) = 0

Combine like terms: -2ix + -2ix = -4ix
(-4ix + -4i2 + -1x2) = 0

Solving
-4ix + -4i2 + -1x2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4ix + 4i2 + x2) = 0

Factor a trinomial.
-1((2i + x)(2i + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2i + x)' equal to zero and attempt to solve:

Simplifying
2i + x = 0

Solving
2i + x = 0

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

Add '-1x' to each side of the equation.
2i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
2i + 0 = 0 + -1x
2i = 0 + -1x
Remove the zero:
2i = -1x

Divide each side by '2'.
i = -0.5x

Simplifying
i = -0.5x

Subproblem 2
Set the factor '(2i + x)' equal to zero and attempt to solve:

Simplifying
2i + x = 0

Solving
2i + x = 0

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

Add '-1x' to each side of the equation.
2i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
2i + 0 = 0 + -1x
2i = 0 + -1x
Remove the zero:
2i = -1x

Divide each side by '2'.
i = -0.5x

Simplifying
i = -0.5x
Solution
i = {-0.5x, -0.5x}

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