(10-8i)(2-3i)=0

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Solution for (10-8i)(2-3i)=0 equation: 


Simplifying
(10 + -8i)(2 + -3i) = 0

Multiply (10 + -8i) * (2 + -3i)
(10(2 + -3i) + -8i * (2 + -3i)) = 0
((2 * 10 + -3i * 10) + -8i * (2 + -3i)) = 0
((20 + -30i) + -8i * (2 + -3i)) = 0
(20 + -30i + (2 * -8i + -3i * -8i)) = 0
(20 + -30i + (-16i + 24i2)) = 0

Combine like terms: -30i + -16i = -46i
(20 + -46i + 24i2) = 0

Solving
20 + -46i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -23i + 12i2) = 0

Factor a trinomial.
2((2 + -3i)(5 + -4i)) = 0

Ignore the factor 2.

Subproblem 1
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 2
Set the factor '(5 + -4i)' equal to zero and attempt to solve:

Simplifying
5 + -4i = 0

Solving
5 + -4i = 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 + -4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4i = 0 + -5
-4i = 0 + -5

Combine like terms: 0 + -5 = -5
-4i = -5

Divide each side by '-4'.
i = 1.25

Simplifying
i = 1.25
Solution
i = {0.6666666667, 1.25}

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