(3+3i)(2-3i)=

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

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

Multiply (3 + 3i) * (2 + -3i)
(3(2 + -3i) + 3i * (2 + -3i)) = 0
((2 * 3 + -3i * 3) + 3i * (2 + -3i)) = 0
((6 + -9i) + 3i * (2 + -3i)) = 0
(6 + -9i + (2 * 3i + -3i * 3i)) = 0
(6 + -9i + (6i + -9i2)) = 0

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

Solving
6 + -3i + -9i2 = 0

Solving for variable 'i'.

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

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

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve:

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
Subproblem 2
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
Solution
i = {0.6666666667, -1}