(12+12i)(3+6i)=

Solution for (12+12i)(3+6i)= equation:

Simplifying
(12 + 12i)(3 + 6i) = 0

Multiply (12 + 12i) * (3 + 6i)
(12(3 + 6i) + 12i * (3 + 6i)) = 0
((3 * 12 + 6i * 12) + 12i * (3 + 6i)) = 0
((36 + 72i) + 12i * (3 + 6i)) = 0
(36 + 72i + (3 * 12i + 6i * 12i)) = 0
(36 + 72i + (36i + 72i2)) = 0

Combine like terms: 72i + 36i = 108i
(36 + 108i + 72i2) = 0

Solving
36 + 108i + 72i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '36'.
36(1 + 3i + 2i2) = 0

Factor a trinomial.
36((1 + i)(1 + 2i)) = 0

Ignore the factor 36.
Subproblem 1
Set the factor '(1 + i)' equal to zero and attempt to solve:

Simplifying
1 + i = 0

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

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

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

Simplifying
i = -1
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 = {-1, -0.5}