(3x-6i)(x+21i)=0

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Solution for (3x-6i)(x+21i)=0 equation: 


Simplifying
(3x + -6i)(x + 21i) = 0

Reorder the terms:
(-6i + 3x)(x + 21i) = 0

Reorder the terms:
(-6i + 3x)(21i + x) = 0

Multiply (-6i + 3x) * (21i + x)
(-6i * (21i + x) + 3x * (21i + x)) = 0
((21i * -6i + x * -6i) + 3x * (21i + x)) = 0

Reorder the terms:
((-6ix + -126i2) + 3x * (21i + x)) = 0
((-6ix + -126i2) + 3x * (21i + x)) = 0
(-6ix + -126i2 + (21i * 3x + x * 3x)) = 0
(-6ix + -126i2 + (63ix + 3x2)) = 0

Reorder the terms:
(-6ix + 63ix + -126i2 + 3x2) = 0

Combine like terms: -6ix + 63ix = 57ix
(57ix + -126i2 + 3x2) = 0

Solving
57ix + -126i2 + 3x2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(19ix + -42i2 + x2) = 0

Factor a trinomial.
3((-21i + -1x)(2i + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-21i + -1x)' equal to zero and attempt to solve:

Simplifying
-21i + -1x = 0

Solving
-21i + -1x = 0

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

Add 'x' to each side of the equation.
-21i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-21i + 0 = 0 + x
-21i = 0 + x
Remove the zero:
-21i = x

Divide each side by '-21'.
i = -0.04761904762x

Simplifying
i = -0.04761904762x

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

Simplifying
2i + -1x = 0

Solving
2i + -1x = 0

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

Add 'x' to each side of the equation.
2i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
2i + 0 = 0 + x
2i = 0 + x
Remove the zero:
2i = x

Divide each side by '2'.
i = 0.5x

Simplifying
i = 0.5x
Solution
i = {-0.04761904762x, 0.5x}

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