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

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

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

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

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

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

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

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

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

Solving
-81i2 + x2 = 0

Solving for variable 'i'.

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

Add '-1x2' to each side of the equation.
-81i2 + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
-81i2 + 0 = 0 + -1x2
-81i2 = 0 + -1x2
Remove the zero:
-81i2 = -1x2

Divide each side by '-81'.
i2 = 0.01234567901x2

Simplifying
i2 = 0.01234567901x2

Take the square root of each side:
i = {-0.111111111x, 0.111111111x}