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

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

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

Multiply (-4 + -8i) * (3 + i)
(-4(3 + i) + -8i * (3 + i)) = 0
((3 * -4 + i * -4) + -8i * (3 + i)) = 0
((-12 + -4i) + -8i * (3 + i)) = 0
(-12 + -4i + (3 * -8i + i * -8i)) = 0
(-12 + -4i + (-24i + -8i2)) = 0

Combine like terms: -4i + -24i = -28i
(-12 + -28i + -8i2) = 0

Solving
-12 + -28i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(3 + 7i + 2i2) = 0

Factor a trinomial.
-4((3 + i)(1 + 2i)) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

Solving
3 + i = 0

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

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

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

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

Simplifying
i = -3
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 = {-3, -0.5}