(-3-8i)(1+2i)=

Solution for (-3-8i)(1+2i)= equation:

Simplifying
(-3 + -8i)(1 + 2i) = 0

Multiply (-3 + -8i) * (1 + 2i)
(-3(1 + 2i) + -8i * (1 + 2i)) = 0
((1 * -3 + 2i * -3) + -8i * (1 + 2i)) = 0
((-3 + -6i) + -8i * (1 + 2i)) = 0
(-3 + -6i + (1 * -8i + 2i * -8i)) = 0
(-3 + -6i + (-8i + -16i2)) = 0

Combine like terms: -6i + -8i = -14i
(-3 + -14i + -16i2) = 0

Solving
-3 + -14i + -16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 14i + 16i2) = 0

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

Ignore the factor -1.
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 '(3 + 8i)' equal to zero and attempt to solve:

Simplifying
3 + 8i = 0

Solving
3 + 8i = 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 + 8i = 0 + -3

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

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

Divide each side by '8'.
i = -0.375

Simplifying
i = -0.375
Solution
i = {-0.5, -0.375}