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

Solution for (3+2j)(-2+4j)= 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}