(-3x+2i)(x-6i)=0

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Solution for (-3x+2i)(x-6i)=0 equation: 


Simplifying
(-3x + 2i)(x + -6i) = 0

Reorder the terms:
(2i + -3x)(x + -6i) = 0

Reorder the terms:
(2i + -3x)(-6i + x) = 0

Multiply (2i + -3x) * (-6i + x)
(2i * (-6i + x) + -3x * (-6i + x)) = 0
((-6i * 2i + x * 2i) + -3x * (-6i + x)) = 0

Reorder the terms:
((2ix + -12i2) + -3x * (-6i + x)) = 0
((2ix + -12i2) + -3x * (-6i + x)) = 0
(2ix + -12i2 + (-6i * -3x + x * -3x)) = 0
(2ix + -12i2 + (18ix + -3x2)) = 0

Reorder the terms:
(2ix + 18ix + -12i2 + -3x2) = 0

Combine like terms: 2ix + 18ix = 20ix
(20ix + -12i2 + -3x2) = 0

Solving
20ix + -12i2 + -3x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-6i + x)(2i + -3x) = 0


Subproblem 1
Set the factor '(-6i + x)' equal to zero and attempt to solve:

Simplifying
-6i + x = 0

Solving
-6i + x = 0

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

Add '-1x' to each side of the equation.
-6i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
-6i + 0 = 0 + -1x
-6i = 0 + -1x
Remove the zero:
-6i = -1x

Divide each side by '-6'.
i = 0.1666666667x

Simplifying
i = 0.1666666667x

Subproblem 2
Set the factor '(2i + -3x)' equal to zero and attempt to solve:

Simplifying
2i + -3x = 0

Solving
2i + -3x = 0

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

Add '3x' to each side of the equation.
2i + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
2i + 0 = 0 + 3x
2i = 0 + 3x
Remove the zero:
2i = 3x

Divide each side by '2'.
i = 1.5x

Simplifying
i = 1.5x
Solution
i = {0.1666666667x, 1.5x}

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