(-10-8i)(-3i-5)=

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Solution for (-10-8i)(-3i-5)= equation: 


Simplifying
(-10 + -8i)(-3i + -5) = 0

Reorder the terms:
(-10 + -8i)(-5 + -3i) = 0

Multiply (-10 + -8i) * (-5 + -3i)
(-10(-5 + -3i) + -8i * (-5 + -3i)) = 0
((-5 * -10 + -3i * -10) + -8i * (-5 + -3i)) = 0
((50 + 30i) + -8i * (-5 + -3i)) = 0
(50 + 30i + (-5 * -8i + -3i * -8i)) = 0
(50 + 30i + (40i + 24i2)) = 0

Combine like terms: 30i + 40i = 70i
(50 + 70i + 24i2) = 0

Solving
50 + 70i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 35i + 12i2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {-1.666666667, -1.25}

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