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

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

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

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

Combine like terms: 2i + -6i = -4i
(6 + -4i + -2i2) = 0

Solving
6 + -4i + -2i2 = 0

Solving for variable 'i'.

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

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

Ignore the factor 2.
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 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

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

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

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

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