(4-3i)(2-i)(3i)=0

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Solution for (4-3i)(2-i)(3i)=0 equation: 


Simplifying
(4 + -3i)(2 + -1i)(3i) = 0

Remove parenthesis around (3i)
(4 + -3i)(2 + -1i) * 3i = 0

Reorder the terms for easier multiplication:
3i(4 + -3i)(2 + -1i) = 0

Multiply (4 + -3i) * (2 + -1i)
3i(4(2 + -1i) + -3i * (2 + -1i)) = 0
3i((2 * 4 + -1i * 4) + -3i * (2 + -1i)) = 0
3i((8 + -4i) + -3i * (2 + -1i)) = 0
3i(8 + -4i + (2 * -3i + -1i * -3i)) = 0
3i(8 + -4i + (-6i + 3i2)) = 0

Combine like terms: -4i + -6i = -10i
3i(8 + -10i + 3i2) = 0
(8 * 3i + -10i * 3i + 3i2 * 3i) = 0
(24i + -30i2 + 9i3) = 0

Solving
24i + -30i2 + 9i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3i'.
3i(8 + -10i + 3i2) = 0

Factor a trinomial.
3i((4 + -3i)(2 + -1i)) = 0

Ignore the factor 3.

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 '(4 + -3i)' equal to zero and attempt to solve:

Simplifying
4 + -3i = 0

Solving
4 + -3i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3i = 0 + -4
-3i = 0 + -4

Combine like terms: 0 + -4 = -4
-3i = -4

Divide each side by '-3'.
i = 1.333333333

Simplifying
i = 1.333333333

Subproblem 3
Set the factor '(2 + -1i)' equal to zero and attempt to solve:

Simplifying
2 + -1i = 0

Solving
2 + -1i = 0

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

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

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2
Solution
i = {0, 1.333333333, 2}

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