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

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

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

Multiply (4 + -8i) * (3 + i)
(4(3 + i) + -8i * (3 + i)) = 0
((3 * 4 + i * 4) + -8i * (3 + i)) = 0
((12 + 4i) + -8i * (3 + i)) = 0
(12 + 4i + (3 * -8i + i * -8i)) = 0
(12 + 4i + (-24i + -8i2)) = 0

Combine like terms: 4i + -24i = -20i
(12 + -20i + -8i2) = 0

Solving
12 + -20i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -5i + -2i2) = 0

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

Ignore the factor 4.
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 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
Solution
i = {0.5, -3}