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

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

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

Multiply (3 + -2j) * (2 + 4j)
(3(2 + 4j) + -2j * (2 + 4j)) = 0
((2 * 3 + 4j * 3) + -2j * (2 + 4j)) = 0
((6 + 12j) + -2j * (2 + 4j)) = 0
(6 + 12j + (2 * -2j + 4j * -2j)) = 0
(6 + 12j + (-4j + -8j2)) = 0

Combine like terms: 12j + -4j = 8j
(6 + 8j + -8j2) = 0

Solving
6 + 8j + -8j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 4j + -4j2) = 0

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

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

Simplifying
3 + -2j = 0

Solving
3 + -2j = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2j = 0 + -3

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

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

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

Simplifying
j = 1.5
Subproblem 2
Set the factor '(1 + 2j)' equal to zero and attempt to solve:

Simplifying
1 + 2j = 0

Solving
1 + 2j = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2j = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2j = 0 + -1
2j = 0 + -1

Combine like terms: 0 + -1 = -1
2j = -1

Divide each side by '2'.
j = -0.5

Simplifying
j = -0.5
Solution
j = {1.5, -0.5}