(-i)(8-3i)(5-6i)=0

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Solution for (-i)(8-3i)(5-6i)=0 equation: 


Simplifying
(-1i)(8 + -3i)(5 + -6i) = 0

Remove parenthesis around (-1i)
-1i(8 + -3i)(5 + -6i) = 0

Multiply (8 + -3i) * (5 + -6i)
-1i(8(5 + -6i) + -3i * (5 + -6i)) = 0
-1i((5 * 8 + -6i * 8) + -3i * (5 + -6i)) = 0
-1i((40 + -48i) + -3i * (5 + -6i)) = 0
-1i(40 + -48i + (5 * -3i + -6i * -3i)) = 0
-1i(40 + -48i + (-15i + 18i2)) = 0

Combine like terms: -48i + -15i = -63i
-1i(40 + -63i + 18i2) = 0
(40 * -1i + -63i * -1i + 18i2 * -1i) = 0
(-40i + 63i2 + -18i3) = 0

Solving
-40i + 63i2 + -18i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'i'.
i(-40 + 63i + -18i2) = 0

Factor a trinomial.
i((-8 + 3i)(5 + -6i)) = 0


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 '(-8 + 3i)' equal to zero and attempt to solve:

Simplifying
-8 + 3i = 0

Solving
-8 + 3i = 0

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

Add '8' to each side of the equation.
-8 + 8 + 3i = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3i = 0 + 8
3i = 0 + 8

Combine like terms: 0 + 8 = 8
3i = 8

Divide each side by '3'.
i = 2.666666667

Simplifying
i = 2.666666667

Subproblem 3
Set the factor '(5 + -6i)' equal to zero and attempt to solve:

Simplifying
5 + -6i = 0

Solving
5 + -6i = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6i = 0 + -5
-6i = 0 + -5

Combine like terms: 0 + -5 = -5
-6i = -5

Divide each side by '-6'.
i = 0.8333333333

Simplifying
i = 0.8333333333
Solution
i = {0, 2.666666667, 0.8333333333}

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