(6+5i)(4-4i)=0

Solution for (6+5i)(4-4i)=0 equation:

Simplifying
(6 + 5i)(4 + -4i) = 0

Multiply (6 + 5i) * (4 + -4i)
(6(4 + -4i) + 5i * (4 + -4i)) = 0
((4 * 6 + -4i * 6) + 5i * (4 + -4i)) = 0
((24 + -24i) + 5i * (4 + -4i)) = 0
(24 + -24i + (4 * 5i + -4i * 5i)) = 0
(24 + -24i + (20i + -20i2)) = 0

Combine like terms: -24i + 20i = -4i
(24 + -4i + -20i2) = 0

Solving
24 + -4i + -20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -1i + -5i2) = 0

Factor a trinomial.
4((1 + -1i)(6 + 5i)) = 0

Ignore the factor 4.
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 '(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
Solution
i = {1, -1.2}