(6+6i)(2-4i)=

Solution for (6+6i)(2-4i)= equation:

Simplifying
(6 + 6i)(2 + -4i) = 0

Multiply (6 + 6i) * (2 + -4i)
(6(2 + -4i) + 6i * (2 + -4i)) = 0
((2 * 6 + -4i * 6) + 6i * (2 + -4i)) = 0
((12 + -24i) + 6i * (2 + -4i)) = 0
(12 + -24i + (2 * 6i + -4i * 6i)) = 0
(12 + -24i + (12i + -24i2)) = 0

Combine like terms: -24i + 12i = -12i
(12 + -12i + -24i2) = 0

Solving
12 + -12i + -24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '12'.
12(1 + -1i + -2i2) = 0

Factor a trinomial.
12((1 + -2i)(1 + i)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve:

Simplifying
1 + i = 0

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

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

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

Simplifying
i = -1
Solution
i = {0.5, -1}