(9x+2i)(3x-2i)=

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Solution for (9x+2i)(3x-2i)= equation: 


Simplifying
(9x + 2i)(3x + -2i) = 0

Reorder the terms:
(2i + 9x)(3x + -2i) = 0

Reorder the terms:
(2i + 9x)(-2i + 3x) = 0

Multiply (2i + 9x) * (-2i + 3x)
(2i * (-2i + 3x) + 9x * (-2i + 3x)) = 0
((-2i * 2i + 3x * 2i) + 9x * (-2i + 3x)) = 0

Reorder the terms:
((6ix + -4i2) + 9x * (-2i + 3x)) = 0
((6ix + -4i2) + 9x * (-2i + 3x)) = 0
(6ix + -4i2 + (-2i * 9x + 3x * 9x)) = 0
(6ix + -4i2 + (-18ix + 27x2)) = 0

Reorder the terms:
(6ix + -18ix + -4i2 + 27x2) = 0

Combine like terms: 6ix + -18ix = -12ix
(-12ix + -4i2 + 27x2) = 0

Solving
-12ix + -4i2 + 27x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-2i + -9x)(2i + -3x) = 0


Subproblem 1
Set the factor '(-2i + -9x)' equal to zero and attempt to solve:

Simplifying
-2i + -9x = 0

Solving
-2i + -9x = 0

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

Add '9x' to each side of the equation.
-2i + -9x + 9x = 0 + 9x

Combine like terms: -9x + 9x = 0
-2i + 0 = 0 + 9x
-2i = 0 + 9x
Remove the zero:
-2i = 9x

Divide each side by '-2'.
i = -4.5x

Simplifying
i = -4.5x

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

Simplifying
2i + -3x = 0

Solving
2i + -3x = 0

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

Add '3x' to each side of the equation.
2i + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
2i + 0 = 0 + 3x
2i = 0 + 3x
Remove the zero:
2i = 3x

Divide each side by '2'.
i = 1.5x

Simplifying
i = 1.5x
Solution
i = {-4.5x, 1.5x}

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