(21-3i)(12i-4i)=0

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Solution for (21-3i)(12i-4i)=0 equation: 


Simplifying
(21 + -3i)(12i + -4i) = 0

Combine like terms: 12i + -4i = 8i
(21 + -3i)(8i) = 0

Remove parenthesis around (8i)
(21 + -3i) * 8i = 0

Reorder the terms for easier multiplication:
8i(21 + -3i) = 0
(21 * 8i + -3i * 8i) = 0
(168i + -24i2) = 0

Solving
168i + -24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '24i'.
24i(7 + -1i) = 0

Ignore the factor 24.

Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0

Subproblem 2
Set the factor '(7 + -1i)' equal to zero and attempt to solve:

Simplifying
7 + -1i = 0

Solving
7 + -1i = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1i = 0 + -7
-1i = 0 + -7

Combine like terms: 0 + -7 = -7
-1i = -7

Divide each side by '-1'.
i = 7

Simplifying
i = 7
Solution
i = {0, 7}

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