(-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 out the Greatest Common Factor (GCF), '-1'.
-1(18ix + 81i2 + x2) = 0

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

Ignore the factor -1.

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 + 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

Solution

i = {-0.1111111111x, -0.1111111111x}

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