(1+2i)x(3-4i)=

Solution for (1+2i)x(3-4i)= equation:

Simplifying
(1 + 2i) * x(3 + -4i) = 0

Reorder the terms for easier multiplication:
x(1 + 2i)(3 + -4i) = 0

Multiply (1 + 2i) * (3 + -4i)
x(1(3 + -4i) + 2i * (3 + -4i)) = 0
x((3 * 1 + -4i * 1) + 2i * (3 + -4i)) = 0
x((3 + -4i) + 2i * (3 + -4i)) = 0
x(3 + -4i + (3 * 2i + -4i * 2i)) = 0
x(3 + -4i + (6i + -8i2)) = 0

Combine like terms: -4i + 6i = 2i
x(3 + 2i + -8i2) = 0
(3 * x + 2i * x + -8i2 * x) = 0

Reorder the terms:
(2ix + -8i2x + 3x) = 0
(2ix + -8i2x + 3x) = 0

Solving
2ix + -8i2x + 3x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2i + -8i2 + 3) = 0

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

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

Simplifying
4i + -3 = 0

Reorder the terms:
-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}