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

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

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

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

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

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

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

Solving
-6 + 1j + j2 = 0

Solving for variable 'j'.

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

Subproblem 1
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
Subproblem 2
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
Solution
j = {-3, 2}