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

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

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

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

Combine like terms: 6i + 3i = 9i
(3 + 9i + 6i2) = 0

Solving
3 + 9i + 6i2 = 0

Solving for variable 'i'.

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

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

Ignore the factor 3.
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}