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

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

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

Reorder the terms:
(-3 + j)(j + -2) = 0

Reorder the terms:
(-3 + j)(-2 + j) = 0

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

Combine like terms: -3j + -2j = -5j
(6 + -5j + j2) = 0

Solving
6 + -5j + j2 = 0

Solving for variable 'j'.

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

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 + -1j)' equal to zero and attempt to solve:

Simplifying
3 + -1j = 0

Solving
3 + -1j = 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 + -1j = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1j = 0 + -3
-1j = 0 + -3

Combine like terms: 0 + -3 = -3
-1j = -3

Divide each side by '-1'.
j = 3

Simplifying
j = 3
Solution
j = {2, 3}