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

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

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

Multiply (3 + -6i) * (6 + -8i)
(3(6 + -8i) + -6i * (6 + -8i)) = 0
((6 * 3 + -8i * 3) + -6i * (6 + -8i)) = 0
((18 + -24i) + -6i * (6 + -8i)) = 0
(18 + -24i + (6 * -6i + -8i * -6i)) = 0
(18 + -24i + (-36i + 48i2)) = 0

Combine like terms: -24i + -36i = -60i
(18 + -60i + 48i2) = 0

Solving
18 + -60i + 48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -10i + 8i2) = 0

Factor a trinomial.
6((1 + -2i)(3 + -4i)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Subproblem 2
Set the factor '(3 + -4i)' equal to zero and attempt to solve:

Simplifying
3 + -4i = 0

Solving
3 + -4i = 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 + -4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4i = 0 + -3
-4i = 0 + -3

Combine like terms: 0 + -3 = -3
-4i = -3

Divide each side by '-4'.
i = 0.75

Simplifying
i = 0.75
Solution
i = {0.5, 0.75}