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

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


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

Multiply (-8 + -6i) * (-5 + -1i)
(-8(-5 + -1i) + -6i * (-5 + -1i)) = 0
((-5 * -8 + -1i * -8) + -6i * (-5 + -1i)) = 0
((40 + 8i) + -6i * (-5 + -1i)) = 0
(40 + 8i + (-5 * -6i + -1i * -6i)) = 0
(40 + 8i + (30i + 6i2)) = 0

Combine like terms: 8i + 30i = 38i
(40 + 38i + 6i2) = 0

Solving
40 + 38i + 6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 19i + 3i2) = 0

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

Ignore the factor 2.

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

Simplifying
5 + i = 0

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

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

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

Simplifying
i = -5

Subproblem 2
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
Solution
i = {-5, -1.333333333}

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