(-2+2i)(6-7i)=0

Solution for (-2+2i)(6-7i)=0 equation:

Simplifying
(-2 + 2i)(6 + -7i) = 0

Multiply (-2 + 2i) * (6 + -7i)
(-2(6 + -7i) + 2i * (6 + -7i)) = 0
((6 * -2 + -7i * -2) + 2i * (6 + -7i)) = 0
((-12 + 14i) + 2i * (6 + -7i)) = 0
(-12 + 14i + (6 * 2i + -7i * 2i)) = 0
(-12 + 14i + (12i + -14i2)) = 0

Combine like terms: 14i + 12i = 26i
(-12 + 26i + -14i2) = 0

Solving
-12 + 26i + -14i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 13i + -7i2) = 0

Factor a trinomial.
2((-1 + i)(6 + -7i)) = 0

Ignore the factor 2.
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 '(6 + -7i)' equal to zero and attempt to solve:

Simplifying
6 + -7i = 0

Solving
6 + -7i = 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 + -7i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7i = 0 + -6
-7i = 0 + -6

Combine like terms: 0 + -6 = -6
-7i = -6

Divide each side by '-7'.
i = 0.8571428571

Simplifying
i = 0.8571428571
Solution
i = {1, 0.8571428571}