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

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

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

Reorder the terms for easier multiplication:
x(4 + -8i)(3 + i) = 0

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

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

Reorder the terms:
(-20ix + -8i2x + 12x) = 0
(-20ix + -8i2x + 12x) = 0

Solving
-20ix + -8i2x + 12x = 0

Solving for variable 'i'.

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

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

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1i + -3)' equal to zero and attempt to solve:

Simplifying
-1i + -3 = 0

Reorder the terms:
-3 + -1i = 0

Solving
-3 + -1i = 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 + -1i = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1i = 0 + 3
-1i = 0 + 3

Combine like terms: 0 + 3 = 3
-1i = 3

Divide each side by '-1'.
i = -3

Simplifying
i = -3
Subproblem 3
Set the factor '(2i + -1)' equal to zero and attempt to solve:

Simplifying
2i + -1 = 0

Reorder the terms:
-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
Solution
i = {-3, 0.5}