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

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

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

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

Combine like terms: -12i + -24i = -36i
(-12 + -36i + -24i2) = 0

Solving
-12 + -36i + -24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-12'.
-12(1 + 3i + 2i2) = 0

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

Ignore the factor -12.
Subproblem 1
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
Subproblem 2
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
Solution
i = {-1, -0.5}