(-7+8i)(6+6i)=0

Solution for (-7+8i)(6+6i)=0 equation:

Simplifying
(-7 + 8i)(6 + 6i) = 0

Multiply (-7 + 8i) * (6 + 6i)
(-7(6 + 6i) + 8i * (6 + 6i)) = 0
((6 * -7 + 6i * -7) + 8i * (6 + 6i)) = 0
((-42 + -42i) + 8i * (6 + 6i)) = 0
(-42 + -42i + (6 * 8i + 6i * 8i)) = 0
(-42 + -42i + (48i + 48i2)) = 0

Combine like terms: -42i + 48i = 6i
(-42 + 6i + 48i2) = 0

Solving
-42 + 6i + 48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + i + 8i2) = 0

Factor a trinomial.
6((-1 + -1i)(7 + -8i)) = 0

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

Simplifying
-1 + -1i = 0

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

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

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

Divide each side by '-1'.
i = -1

Simplifying
i = -1
Subproblem 2
Set the factor '(7 + -8i)' equal to zero and attempt to solve:

Simplifying
7 + -8i = 0

Solving
7 + -8i = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8i = 0 + -7
-8i = 0 + -7

Combine like terms: 0 + -7 = -7
-8i = -7

Divide each side by '-8'.
i = 0.875

Simplifying
i = 0.875
Solution
i = {-1, 0.875}