(3+2i)(-2+4i)=0

Solution for (3+2i)(-2+4i)=0 equation:

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

Multiply (3 + 2i) * (-2 + 4i)
(3(-2 + 4i) + 2i * (-2 + 4i)) = 0
((-2 * 3 + 4i * 3) + 2i * (-2 + 4i)) = 0
((-6 + 12i) + 2i * (-2 + 4i)) = 0
(-6 + 12i + (-2 * 2i + 4i * 2i)) = 0
(-6 + 12i + (-4i + 8i2)) = 0

Combine like terms: 12i + -4i = 8i
(-6 + 8i + 8i2) = 0

Solving
-6 + 8i + 8i2 = 0

Solving for variable 'i'.

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

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

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

Simplifying
-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
Subproblem 2
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
Solution
i = {-1.5, 0.5}