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

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

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

Multiply (2 + -2i) * (3 + 4i)
(2(3 + 4i) + -2i * (3 + 4i)) = 0
((3 * 2 + 4i * 2) + -2i * (3 + 4i)) = 0
((6 + 8i) + -2i * (3 + 4i)) = 0
(6 + 8i + (3 * -2i + 4i * -2i)) = 0
(6 + 8i + (-6i + -8i2)) = 0

Combine like terms: 8i + -6i = 2i
(6 + 2i + -8i2) = 0

Solving
6 + 2i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + i + -4i2) = 0

Factor a trinomial.
2((1 + -1i)(3 + 4i)) = 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 + 4i)' equal to zero and attempt to solve:

Simplifying
3 + 4i = 0

Solving
3 + 4i = 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 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Solution
i = {1, -0.75}