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

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

Simplifying
2(2 + -1j)(3 + 2j) = 0

Multiply (2 + -1j) * (3 + 2j)
2(2(3 + 2j) + -1j * (3 + 2j)) = 0
2((3 * 2 + 2j * 2) + -1j * (3 + 2j)) = 0
2((6 + 4j) + -1j * (3 + 2j)) = 0
2(6 + 4j + (3 * -1j + 2j * -1j)) = 0
2(6 + 4j + (-3j + -2j2)) = 0

Combine like terms: 4j + -3j = 1j
2(6 + 1j + -2j2) = 0
(6 * 2 + 1j * 2 + -2j2 * 2) = 0
(12 + 2j + -4j2) = 0

Solving
12 + 2j + -4j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + j + -2j2) = 0

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

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

Simplifying
2 + -1j = 0

Solving
2 + -1j = 0

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

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

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

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

Divide each side by '-1'.
j = 2

Simplifying
j = 2
Subproblem 2
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
Solution
j = {2, -1.5}