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

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

Simplifying
(4 + -4i)(6 + -1i) = 0

Multiply (4 + -4i) * (6 + -1i)
(4(6 + -1i) + -4i * (6 + -1i)) = 0
((6 * 4 + -1i * 4) + -4i * (6 + -1i)) = 0
((24 + -4i) + -4i * (6 + -1i)) = 0
(24 + -4i + (6 * -4i + -1i * -4i)) = 0
(24 + -4i + (-24i + 4i2)) = 0

Combine like terms: -4i + -24i = -28i
(24 + -28i + 4i2) = 0

Solving
24 + -28i + 4i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -7i + i2) = 0

Factor a trinomial.
4((1 + -1i)(6 + -1i)) = 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 + -1i)' equal to zero and attempt to solve:

Simplifying
6 + -1i = 0

Solving
6 + -1i = 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 + -1i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1i = 0 + -6
-1i = 0 + -6

Combine like terms: 0 + -6 = -6
-1i = -6

Divide each side by '-1'.
i = 6

Simplifying
i = 6
Solution
i = {1, 6}