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

Solution for (-3+2i)(4-4i)=0 equation:

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

Multiply (-3 + 2i) * (4 + -4i)
(-3(4 + -4i) + 2i * (4 + -4i)) = 0
((4 * -3 + -4i * -3) + 2i * (4 + -4i)) = 0
((-12 + 12i) + 2i * (4 + -4i)) = 0
(-12 + 12i + (4 * 2i + -4i * 2i)) = 0
(-12 + 12i + (8i + -8i2)) = 0

Combine like terms: 12i + 8i = 20i
(-12 + 20i + -8i2) = 0

Solving
-12 + 20i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 5i + -2i2) = 0

Factor a trinomial.
4((-3 + 2i)(1 + -1i)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + 2i)' equal to zero and attempt to solve:

Simplifying
-3 + 2i = 0

Solving
-3 + 2i = 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 + 2i = 0 + 3

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

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

Divide each side by '2'.
i = 1.5

Simplifying
i = 1.5
Subproblem 2
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
Solution
i = {1.5, 1}