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

Solution for (4-6i)(3-8i)= 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 = -50i
(12 + -50i + 48i2) = 0

Solving
12 + -50i + 48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -25i + 24i2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
i = {0.375, 0.6666666667}