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

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


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

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

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

Multiply (-6 + -3x) * (2i + x)
(-6(2i + x) + -3x * (2i + x)) = 0
((2i * -6 + x * -6) + -3x * (2i + x)) = 0
((-12i + -6x) + -3x * (2i + x)) = 0
(-12i + -6x + (2i * -3x + x * -3x)) = 0
(-12i + -6x + (-6ix + -3x2)) = 0

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

Solving
-12i + -6ix + -6x + -3x2 = 0

Solving for variable 'i'.

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

Add '6x' to each side of the equation.
-12i + -6ix + -6x + 6x + -3x2 = 0 + 6x

Combine like terms: -6x + 6x = 0
-12i + -6ix + 0 + -3x2 = 0 + 6x
-12i + -6ix + -3x2 = 0 + 6x
Remove the zero:
-12i + -6ix + -3x2 = 6x

Add '3x2' to each side of the equation.
-12i + -6ix + -3x2 + 3x2 = 6x + 3x2

Combine like terms: -3x2 + 3x2 = 0
-12i + -6ix + 0 = 6x + 3x2
-12i + -6ix = 6x + 3x2

Reorder the terms:
-12i + -6ix + -6x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
-12i + -6ix + -6x + -3x2 = 0 + 3x2 + -3x2
-12i + -6ix + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12i + -6ix + -6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(4i + 2ix + 2x + x2) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(4i + 2ix + 2x + x2)' equal to zero and attempt to solve:

Simplifying
4i + 2ix + 2x + x2 = 0

Solving
4i + 2ix + 2x + x2 = 0

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

Add '-2x' to each side of the equation.
4i + 2ix + 2x + -2x + x2 = 0 + -2x

Combine like terms: 2x + -2x = 0
4i + 2ix + 0 + x2 = 0 + -2x
4i + 2ix + x2 = 0 + -2x
Remove the zero:
4i + 2ix + x2 = -2x

Add '-1x2' to each side of the equation.
4i + 2ix + x2 + -1x2 = -2x + -1x2

Combine like terms: x2 + -1x2 = 0
4i + 2ix + 0 = -2x + -1x2
4i + 2ix = -2x + -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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