(-6-5i)(1+3i)=0

Solution for (-6-5i)(1+3i)=0 equation:

Simplifying
(-6 + -5i)(1 + 3i) = 0

Multiply (-6 + -5i) * (1 + 3i)
(-6(1 + 3i) + -5i * (1 + 3i)) = 0
((1 * -6 + 3i * -6) + -5i * (1 + 3i)) = 0
((-6 + -18i) + -5i * (1 + 3i)) = 0
(-6 + -18i + (1 * -5i + 3i * -5i)) = 0
(-6 + -18i + (-5i + -15i2)) = 0

Combine like terms: -18i + -5i = -23i
(-6 + -23i + -15i2) = 0

Solving
-6 + -23i + -15i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 23i + 15i2) = 0

Factor a trinomial.
-1((6 + 5i)(1 + 3i)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 5i)' equal to zero and attempt to solve:

Simplifying
6 + 5i = 0

Solving
6 + 5i = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5i = 0 + -6
5i = 0 + -6

Combine like terms: 0 + -6 = -6
5i = -6

Divide each side by '5'.
i = -1.2

Simplifying
i = -1.2
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 = {-1.2, -0.3333333333}