(6+2i)(3+6i)=0

Solution for (6+2i)(3+6i)=0 equation:

Simplifying
(6 + 2i)(3 + 6i) = 0

Multiply (6 + 2i) * (3 + 6i)
(6(3 + 6i) + 2i * (3 + 6i)) = 0
((3 * 6 + 6i * 6) + 2i * (3 + 6i)) = 0
((18 + 36i) + 2i * (3 + 6i)) = 0
(18 + 36i + (3 * 2i + 6i * 2i)) = 0
(18 + 36i + (6i + 12i2)) = 0

Combine like terms: 36i + 6i = 42i
(18 + 42i + 12i2) = 0

Solving
18 + 42i + 12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 7i + 2i2) = 0

Factor a trinomial.
6((3 + i)(1 + 2i)) = 0

Ignore the factor 6.
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}