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

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


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

Multiply (-5 + 3i) * (-8 + 6i)
(-5(-8 + 6i) + 3i * (-8 + 6i)) = 0
((-8 * -5 + 6i * -5) + 3i * (-8 + 6i)) = 0
((40 + -30i) + 3i * (-8 + 6i)) = 0
(40 + -30i + (-8 * 3i + 6i * 3i)) = 0
(40 + -30i + (-24i + 18i2)) = 0

Combine like terms: -30i + -24i = -54i
(40 + -54i + 18i2) = 0

Solving
40 + -54i + 18i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -27i + 9i2) = 0

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

Ignore the factor 2.

Subproblem 1
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 2
Set the factor '(5 + -3i)' equal to zero and attempt to solve:

Simplifying
5 + -3i = 0

Solving
5 + -3i = 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 + -3i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3i = 0 + -5
-3i = 0 + -5

Combine like terms: 0 + -5 = -5
-3i = -5

Divide each side by '-3'.
i = 1.666666667

Simplifying
i = 1.666666667
Solution
i = {1.333333333, 1.666666667}

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