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

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Solution for (3x+9i)(x+3i)=0 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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