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

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


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

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

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

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

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

Reorder the terms:
(-9ix + 4ix + -18i2 + 2x2) = 0

Combine like terms: -9ix + 4ix = -5ix
(-5ix + -18i2 + 2x2) = 0

Solving
-5ix + -18i2 + 2x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-2i + -1x)(9i + -2x) = 0


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

Simplifying
-2i + -1x = 0

Solving
-2i + -1x = 0

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

Add 'x' to each side of the equation.
-2i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-2i + 0 = 0 + x
-2i = 0 + x
Remove the zero:
-2i = x

Divide each side by '-2'.
i = -0.5x

Simplifying
i = -0.5x

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

Simplifying
9i + -2x = 0

Solving
9i + -2x = 0

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

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

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

Divide each side by '9'.
i = 0.2222222222x

Simplifying
i = 0.2222222222x
Solution
i = {-0.5x, 0.2222222222x}

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