(6-5i)(7+7i)=0

Solution for (6-5i)(7+7i)=0 equation:

Simplifying
(6 + -5i)(7 + 7i) = 0

Multiply (6 + -5i) * (7 + 7i)
(6(7 + 7i) + -5i * (7 + 7i)) = 0
((7 * 6 + 7i * 6) + -5i * (7 + 7i)) = 0
((42 + 42i) + -5i * (7 + 7i)) = 0
(42 + 42i + (7 * -5i + 7i * -5i)) = 0
(42 + 42i + (-35i + -35i2)) = 0

Combine like terms: 42i + -35i = 7i
(42 + 7i + -35i2) = 0

Solving
42 + 7i + -35i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '7'.
7(6 + i + -5i2) = 0

Factor a trinomial.
7((6 + -5i)(1 + i)) = 0

Ignore the factor 7.
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}