(2+4i)(3+3i)=0

Solution for (2+4i)(3+3i)=0 equation:

Simplifying
(2 + 4i)(3 + 3i) = 0

Multiply (2 + 4i) * (3 + 3i)
(2(3 + 3i) + 4i * (3 + 3i)) = 0
((3 * 2 + 3i * 2) + 4i * (3 + 3i)) = 0
((6 + 6i) + 4i * (3 + 3i)) = 0
(6 + 6i + (3 * 4i + 3i * 4i)) = 0
(6 + 6i + (12i + 12i2)) = 0

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

Solving
6 + 18i + 12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 3i + 2i2) = 0

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

Ignore the factor 6.
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}