(2-2i)(9-3i)=

Solution for (2-2i)(9-3i)= equation:

Simplifying
(2 + -2i)(9 + -3i) = 0

Multiply (2 + -2i) * (9 + -3i)
(2(9 + -3i) + -2i * (9 + -3i)) = 0
((9 * 2 + -3i * 2) + -2i * (9 + -3i)) = 0
((18 + -6i) + -2i * (9 + -3i)) = 0
(18 + -6i + (9 * -2i + -3i * -2i)) = 0
(18 + -6i + (-18i + 6i2)) = 0

Combine like terms: -6i + -18i = -24i
(18 + -24i + 6i2) = 0

Solving
18 + -24i + 6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -4i + i2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve:

Simplifying
1 + -1i = 0

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

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

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

Divide each side by '-1'.
i = 1

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

Simplifying
3 + -1i = 0

Solving
3 + -1i = 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 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Solution
i = {1, 3}