(-4-8i)(3+9i)=

Solution for (-4-8i)(3+9i)= equation:

Simplifying
(-4 + -8i)(3 + 9i) = 0

Multiply (-4 + -8i) * (3 + 9i)
(-4(3 + 9i) + -8i * (3 + 9i)) = 0
((3 * -4 + 9i * -4) + -8i * (3 + 9i)) = 0
((-12 + -36i) + -8i * (3 + 9i)) = 0
(-12 + -36i + (3 * -8i + 9i * -8i)) = 0
(-12 + -36i + (-24i + -72i2)) = 0

Combine like terms: -36i + -24i = -60i
(-12 + -60i + -72i2) = 0

Solving
-12 + -60i + -72i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-12'.
-12(1 + 5i + 6i2) = 0

Factor a trinomial.
-12((1 + 2i)(1 + 3i)) = 0

Ignore the factor -12.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 3i)' equal to zero and attempt to solve:

Simplifying
1 + 3i = 0

Solving
1 + 3i = 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 + 3i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3i = 0 + -1
3i = 0 + -1

Combine like terms: 0 + -1 = -1
3i = -1

Divide each side by '3'.
i = -0.3333333333

Simplifying
i = -0.3333333333
Solution
i = {-0.5, -0.3333333333}