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

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

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

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

Multiply (-4 + 4i) * (3 + 2i)
x(-4(3 + 2i) + 4i * (3 + 2i)) = 0
x((3 * -4 + 2i * -4) + 4i * (3 + 2i)) = 0
x((-12 + -8i) + 4i * (3 + 2i)) = 0
x(-12 + -8i + (3 * 4i + 2i * 4i)) = 0
x(-12 + -8i + (12i + 8i2)) = 0

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

Reorder the terms:
(4ix + 8i2x + -12x) = 0
(4ix + 8i2x + -12x) = 0

Solving
4ix + 8i2x + -12x = 0

Solving for variable 'i'.

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

Factor a trinomial.
4x((i + -1)(2i + 3)) = 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 '(i + -1)' equal to zero and attempt to solve:

Simplifying
i + -1 = 0

Reorder the terms:
-1 + i = 0

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

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

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

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

Simplifying
2i + 3 = 0

Reorder the terms:
3 + 2i = 0

Solving
3 + 2i = 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 + 2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2i = 0 + -3
2i = 0 + -3

Combine like terms: 0 + -3 = -3
2i = -3

Divide each side by '2'.
i = -1.5

Simplifying
i = -1.5
Solution
i = {1, -1.5}