(6+4i)(4-4i)=

Solution for (6+4i)(4-4i)= equation:

Simplifying
(6 + 4i)(4 + -4i) = 0

Multiply (6 + 4i) * (4 + -4i)
(6(4 + -4i) + 4i * (4 + -4i)) = 0
((4 * 6 + -4i * 6) + 4i * (4 + -4i)) = 0
((24 + -24i) + 4i * (4 + -4i)) = 0
(24 + -24i + (4 * 4i + -4i * 4i)) = 0
(24 + -24i + (16i + -16i2)) = 0

Combine like terms: -24i + 16i = -8i
(24 + -8i + -16i2) = 0

Solving
24 + -8i + -16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '8'.
8(3 + -1i + -2i2) = 0

Factor a trinomial.
8((1 + -1i)(3 + 2i)) = 0

Ignore the factor 8.
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 + 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
Solution
i = {1, -1.5}