(4-6i)(3+8i)=0

Solution for (4-6i)(3+8i)=0 equation:

Simplifying
(4 + -6i)(3 + 8i) = 0

Multiply (4 + -6i) * (3 + 8i)
(4(3 + 8i) + -6i * (3 + 8i)) = 0
((3 * 4 + 8i * 4) + -6i * (3 + 8i)) = 0
((12 + 32i) + -6i * (3 + 8i)) = 0
(12 + 32i + (3 * -6i + 8i * -6i)) = 0
(12 + 32i + (-18i + -48i2)) = 0

Combine like terms: 32i + -18i = 14i
(12 + 14i + -48i2) = 0

Solving
12 + 14i + -48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 7i + -24i2) = 0

Factor a trinomial.
2((2 + -3i)(3 + 8i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve:

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
Subproblem 2
Set the factor '(3 + 8i)' equal to zero and attempt to solve:

Simplifying
3 + 8i = 0

Solving
3 + 8i = 0

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

Add '-3' to each side of the equation.
3 + -3 + 8i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8i = 0 + -3
8i = 0 + -3

Combine like terms: 0 + -3 = -3
8i = -3

Divide each side by '8'.
i = -0.375

Simplifying
i = -0.375
Solution
i = {0.6666666667, -0.375}