(5-2i)(6-8i)=

Solution for (5-2i)(6-8i)= equation:

Simplifying
(5 + -2i)(6 + -8i) = 0

Multiply (5 + -2i) * (6 + -8i)
(5(6 + -8i) + -2i * (6 + -8i)) = 0
((6 * 5 + -8i * 5) + -2i * (6 + -8i)) = 0
((30 + -40i) + -2i * (6 + -8i)) = 0
(30 + -40i + (6 * -2i + -8i * -2i)) = 0
(30 + -40i + (-12i + 16i2)) = 0

Combine like terms: -40i + -12i = -52i
(30 + -52i + 16i2) = 0

Solving
30 + -52i + 16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -26i + 8i2) = 0

Factor a trinomial.
2((3 + -4i)(5 + -2i)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -2i)' equal to zero and attempt to solve:

Simplifying
5 + -2i = 0

Solving
5 + -2i = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2i = 0 + -5
-2i = 0 + -5

Combine like terms: 0 + -5 = -5
-2i = -5

Divide each side by '-2'.
i = 2.5

Simplifying
i = 2.5
Solution
i = {0.75, 2.5}