(3i)(2-3i)(7-6i)=

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Solution for (3i)(2-3i)(7-6i)= equation: 


Simplifying
(3i)(2 + -3i)(7 + -6i) = 0

Remove parenthesis around (3i)
3i(2 + -3i)(7 + -6i) = 0

Multiply (2 + -3i) * (7 + -6i)
3i(2(7 + -6i) + -3i * (7 + -6i)) = 0
3i((7 * 2 + -6i * 2) + -3i * (7 + -6i)) = 0
3i((14 + -12i) + -3i * (7 + -6i)) = 0
3i(14 + -12i + (7 * -3i + -6i * -3i)) = 0
3i(14 + -12i + (-21i + 18i2)) = 0

Combine like terms: -12i + -21i = -33i
3i(14 + -33i + 18i2) = 0
(14 * 3i + -33i * 3i + 18i2 * 3i) = 0
(42i + -99i2 + 54i3) = 0

Solving
42i + -99i2 + 54i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3i'.
3i(14 + -33i + 18i2) = 0

Factor a trinomial.
3i((2 + -3i)(7 + -6i)) = 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 '(2 + -3i)' equal to zero and attempt to solve:

Simplifying
2 + -3i = 0

Solving
2 + -3i = 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 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667

Subproblem 3
Set the factor '(7 + -6i)' equal to zero and attempt to solve:

Simplifying
7 + -6i = 0

Solving
7 + -6i = 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 + -6i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6i = 0 + -7
-6i = 0 + -7

Combine like terms: 0 + -7 = -7
-6i = -7

Divide each side by '-6'.
i = 1.166666667

Simplifying
i = 1.166666667
Solution
i = {0, 0.6666666667, 1.166666667}

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