(a+2)(a+3)=2

Solution for (a+2)(a+3)=2 equation:

Simplifying
(a + 2)(a + 3) = 2

Reorder the terms:
(2 + a)(a + 3) = 2

Reorder the terms:
(2 + a)(3 + a) = 2

Multiply (2 + a) * (3 + a)
(2(3 + a) + a(3 + a)) = 2
((3 * 2 + a * 2) + a(3 + a)) = 2
((6 + 2a) + a(3 + a)) = 2
(6 + 2a + (3 * a + a * a)) = 2
(6 + 2a + (3a + a2)) = 2

Combine like terms: 2a + 3a = 5a
(6 + 5a + a2) = 2

Solving
6 + 5a + a2 = 2

Solving for variable 'a'.

Reorder the terms:
6 + -2 + 5a + a2 = 2 + -2

Combine like terms: 6 + -2 = 4
4 + 5a + a2 = 2 + -2

Combine like terms: 2 + -2 = 0
4 + 5a + a2 = 0

Factor a trinomial.
(4 + a)(1 + a) = 0

Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

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

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

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

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

Simplifying
a = -1
Solution
a = {-4, -1}