(5-8i)(4-6i)=0

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Solution for (5-8i)(4-6i)=0 equation: 


Simplifying
(5 + -8i)(4 + -6i) = 0

Multiply (5 + -8i) * (4 + -6i)
(5(4 + -6i) + -8i * (4 + -6i)) = 0
((4 * 5 + -6i * 5) + -8i * (4 + -6i)) = 0
((20 + -30i) + -8i * (4 + -6i)) = 0
(20 + -30i + (4 * -8i + -6i * -8i)) = 0
(20 + -30i + (-32i + 48i2)) = 0

Combine like terms: -30i + -32i = -62i
(20 + -62i + 48i2) = 0

Solving
20 + -62i + 48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -31i + 24i2) = 0

Factor a trinomial.
2((5 + -8i)(2 + -3i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -8i)' equal to zero and attempt to solve:

Simplifying
5 + -8i = 0

Solving
5 + -8i = 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 + -8i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8i = 0 + -5
-8i = 0 + -5

Combine like terms: 0 + -5 = -5
-8i = -5

Divide each side by '-8'.
i = 0.625

Simplifying
i = 0.625

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
Solution
i = {0.625, 0.6666666667}

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