(-8-3i)(2+4i)=0

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Solution for (-8-3i)(2+4i)=0 equation: 


Simplifying
(-8 + -3i)(2 + 4i) = 0

Multiply (-8 + -3i) * (2 + 4i)
(-8(2 + 4i) + -3i * (2 + 4i)) = 0
((2 * -8 + 4i * -8) + -3i * (2 + 4i)) = 0
((-16 + -32i) + -3i * (2 + 4i)) = 0
(-16 + -32i + (2 * -3i + 4i * -3i)) = 0
(-16 + -32i + (-6i + -12i2)) = 0

Combine like terms: -32i + -6i = -38i
(-16 + -38i + -12i2) = 0

Solving
-16 + -38i + -12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(8 + 19i + 6i2) = 0

Factor a trinomial.
-2((8 + 3i)(1 + 2i)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(8 + 3i)' equal to zero and attempt to solve:

Simplifying
8 + 3i = 0

Solving
8 + 3i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + 3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3i = 0 + -8
3i = 0 + -8

Combine like terms: 0 + -8 = -8
3i = -8

Divide each side by '3'.
i = -2.666666667

Simplifying
i = -2.666666667

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

Simplifying
1 + 2i = 0

Solving
1 + 2i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2i = 0 + -1
2i = 0 + -1

Combine like terms: 0 + -1 = -1
2i = -1

Divide each side by '2'.
i = -0.5

Simplifying
i = -0.5
Solution
i = {-2.666666667, -0.5}

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