(x+3i)(x+3i)=

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


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

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

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

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

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

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

Combine like terms: 3ix + 3ix = 6ix
(6ix + 9i2 + x2) = 0

Solving
6ix + 9i2 + x2 = 0

Solving for variable 'i'.

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


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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