(-3x-9i)(x+3i)=

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Solution for (-3x-9i)(x+3i)= equation: 


Simplifying
(-3x + -9i)(x + 3i) = 0

Reorder the terms:
(-9i + -3x)(x + 3i) = 0

Reorder the terms:
(-9i + -3x)(3i + x) = 0

Multiply (-9i + -3x) * (3i + x)
(-9i * (3i + x) + -3x * (3i + x)) = 0
((3i * -9i + x * -9i) + -3x * (3i + x)) = 0

Reorder the terms:
((-9ix + -27i2) + -3x * (3i + x)) = 0
((-9ix + -27i2) + -3x * (3i + x)) = 0
(-9ix + -27i2 + (3i * -3x + x * -3x)) = 0
(-9ix + -27i2 + (-9ix + -3x2)) = 0

Reorder the terms:
(-9ix + -9ix + -27i2 + -3x2) = 0

Combine like terms: -9ix + -9ix = -18ix
(-18ix + -27i2 + -3x2) = 0

Solving
-18ix + -27i2 + -3x2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(6ix + 9i2 + x2) = 0

Factor a trinomial.
-3((3i + x)(3i + x)) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(3i + x)' equal to zero and attempt to solve:

Simplifying
3i + x = 0

Solving
3i + x = 0

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

Add '-1x' to each side of the equation.
3i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
3i + 0 = 0 + -1x
3i = 0 + -1x
Remove the zero:
3i = -1x

Divide each side by '3'.
i = -0.3333333333x

Simplifying
i = -0.3333333333x

Subproblem 2
Set the factor '(3i + x)' equal to zero and attempt to solve:

Simplifying
3i + x = 0

Solving
3i + x = 0

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

Add '-1x' to each side of the equation.
3i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
3i + 0 = 0 + -1x
3i = 0 + -1x
Remove the zero:
3i = -1x

Divide each side by '3'.
i = -0.3333333333x

Simplifying
i = -0.3333333333x
Solution
i = {-0.3333333333x, -0.3333333333x}

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