(x+3i)(x-5i)=0

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Solution for (x+3i)(x-5i)=0 equation: 


Simplifying
(x + 3i)(x + -5i) = 0

Reorder the terms:
(3i + x)(x + -5i) = 0

Reorder the terms:
(3i + x)(-5i + x) = 0

Multiply (3i + x) * (-5i + x)
(3i * (-5i + x) + x(-5i + x)) = 0
((-5i * 3i + x * 3i) + x(-5i + x)) = 0

Reorder the terms:
((3ix + -15i2) + x(-5i + x)) = 0
((3ix + -15i2) + x(-5i + x)) = 0
(3ix + -15i2 + (-5i * x + x * x)) = 0
(3ix + -15i2 + (-5ix + x2)) = 0

Reorder the terms:
(3ix + -5ix + -15i2 + x2) = 0

Combine like terms: 3ix + -5ix = -2ix
(-2ix + -15i2 + x2) = 0

Solving
-2ix + -15i2 + x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-3i + -1x)(5i + -1x) = 0


Subproblem 1
Set the factor '(-3i + -1x)' equal to zero and attempt to solve:

Simplifying
-3i + -1x = 0

Solving
-3i + -1x = 0

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

Add 'x' to each side of the equation.
-3i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-3i + 0 = 0 + x
-3i = 0 + x
Remove the zero:
-3i = x

Divide each side by '-3'.
i = -0.3333333333x

Simplifying
i = -0.3333333333x

Subproblem 2
Set the factor '(5i + -1x)' equal to zero and attempt to solve:

Simplifying
5i + -1x = 0

Solving
5i + -1x = 0

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

Add 'x' to each side of the equation.
5i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
5i + 0 = 0 + x
5i = 0 + x
Remove the zero:
5i = x

Divide each side by '5'.
i = 0.2x

Simplifying
i = 0.2x
Solution
i = {-0.3333333333x, 0.2x}

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