(2+2i)(6+5i)=0

Solution for (2+2i)(6+5i)=0 equation:

Simplifying
(2 + 2i)(6 + 5i) = 0

Multiply (2 + 2i) * (6 + 5i)
(2(6 + 5i) + 2i * (6 + 5i)) = 0
((6 * 2 + 5i * 2) + 2i * (6 + 5i)) = 0
((12 + 10i) + 2i * (6 + 5i)) = 0
(12 + 10i + (6 * 2i + 5i * 2i)) = 0
(12 + 10i + (12i + 10i2)) = 0

Combine like terms: 10i + 12i = 22i
(12 + 22i + 10i2) = 0

Solving
12 + 22i + 10i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 11i + 5i2) = 0

Factor a trinomial.
2((6 + 5i)(1 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 5i)' equal to zero and attempt to solve:

Simplifying
6 + 5i = 0

Solving
6 + 5i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + 5i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5i = 0 + -6
5i = 0 + -6

Combine like terms: 0 + -6 = -6
5i = -6

Divide each side by '5'.
i = -1.2

Simplifying
i = -1.2
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 = {-1.2, -1}