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

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

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

Reorder the terms:
(3 + Z)(Z + 2) + -1(Z + 3) = 0

Reorder the terms:
(3 + Z)(2 + Z) + -1(Z + 3) = 0

Multiply (3 + Z) * (2 + Z)
(3(2 + Z) + Z(2 + Z)) + -1(Z + 3) = 0
((2 * 3 + Z * 3) + Z(2 + Z)) + -1(Z + 3) = 0
((6 + 3Z) + Z(2 + Z)) + -1(Z + 3) = 0
(6 + 3Z + (2 * Z + Z * Z)) + -1(Z + 3) = 0
(6 + 3Z + (2Z + Z2)) + -1(Z + 3) = 0

Combine like terms: 3Z + 2Z = 5Z
(6 + 5Z + Z2) + -1(Z + 3) = 0

Reorder the terms:
6 + 5Z + Z2 + -1(3 + Z) = 0
6 + 5Z + Z2 + (3 * -1 + Z * -1) = 0
6 + 5Z + Z2 + (-3 + -1Z) = 0

Reorder the terms:
6 + -3 + 5Z + -1Z + Z2 = 0

Combine like terms: 6 + -3 = 3
3 + 5Z + -1Z + Z2 = 0

Combine like terms: 5Z + -1Z = 4Z
3 + 4Z + Z2 = 0

Solving
3 + 4Z + Z2 = 0

Solving for variable 'Z'.

Factor a trinomial.
(3 + Z)(1 + Z) = 0

Subproblem 1
Set the factor '(3 + Z)' equal to zero and attempt to solve:

Simplifying
3 + Z = 0

Solving
3 + Z = 0

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

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

Combine like terms: 3 + -3 = 0
0 + Z = 0 + -3
Z = 0 + -3

Combine like terms: 0 + -3 = -3
Z = -3

Simplifying
Z = -3
Subproblem 2
Set the factor '(1 + Z)' equal to zero and attempt to solve:

Simplifying
1 + Z = 0

Solving
1 + Z = 0

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

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

Combine like terms: 1 + -1 = 0
0 + Z = 0 + -1
Z = 0 + -1

Combine like terms: 0 + -1 = -1
Z = -1

Simplifying
Z = -1
Solution
Z = {-3, -1}