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

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Solution for (-x+9i)(x-9i)=0 equation: 


Simplifying
(-1x + 9i)(x + -9i) = 0

Reorder the terms:
(9i + -1x)(x + -9i) = 0

Reorder the terms:
(9i + -1x)(-9i + x) = 0

Multiply (9i + -1x) * (-9i + x)
(9i * (-9i + x) + -1x * (-9i + x)) = 0
((-9i * 9i + x * 9i) + -1x * (-9i + x)) = 0

Reorder the terms:
((9ix + -81i2) + -1x * (-9i + x)) = 0
((9ix + -81i2) + -1x * (-9i + x)) = 0
(9ix + -81i2 + (-9i * -1x + x * -1x)) = 0
(9ix + -81i2 + (9ix + -1x2)) = 0

Reorder the terms:
(9ix + 9ix + -81i2 + -1x2) = 0

Combine like terms: 9ix + 9ix = 18ix
(18ix + -81i2 + -1x2) = 0

Solving
18ix + -81i2 + -1x2 = 0

Solving for variable 'i'.

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


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

Simplifying
-9i + x = 0

Solving
-9i + x = 0

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

Add '-1x' to each side of the equation.
-9i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
-9i + 0 = 0 + -1x
-9i = 0 + -1x
Remove the zero:
-9i = -1x

Divide each side by '-9'.
i = 0.1111111111x

Simplifying
i = 0.1111111111x

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

Simplifying
9i + -1x = 0

Solving
9i + -1x = 0

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

Add 'x' to each side of the equation.
9i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
9i + 0 = 0 + x
9i = 0 + x
Remove the zero:
9i = x

Divide each side by '9'.
i = 0.1111111111x

Simplifying
i = 0.1111111111x
Solution
i = {0.1111111111x, 0.1111111111x}

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