(-3+6i)(2-8i)=

Solution for (-3+6i)(2-8i)= equation:

Simplifying
(-3 + 6i)(2 + -8i) = 0

Multiply (-3 + 6i) * (2 + -8i)
(-3(2 + -8i) + 6i * (2 + -8i)) = 0
((2 * -3 + -8i * -3) + 6i * (2 + -8i)) = 0
((-6 + 24i) + 6i * (2 + -8i)) = 0
(-6 + 24i + (2 * 6i + -8i * 6i)) = 0
(-6 + 24i + (12i + -48i2)) = 0

Combine like terms: 24i + 12i = 36i
(-6 + 36i + -48i2) = 0

Solving
-6 + 36i + -48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 6i + -8i2) = 0

Factor a trinomial.
6((-1 + 2i)(1 + -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 '(1 + -4i)' equal to zero and attempt to solve:

Simplifying
1 + -4i = 0

Solving
1 + -4i = 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 + -4i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4i = 0 + -1
-4i = 0 + -1

Combine like terms: 0 + -1 = -1
-4i = -1

Divide each side by '-4'.
i = 0.25

Simplifying
i = 0.25
Solution
i = {0.5, 0.25}