(x+2)(x+3)=2

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

Simplifying
(x + 2)(x + 3) = 2

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

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

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 2
((3 * 2 + x * 2) + x(3 + x)) = 2
((6 + 2x) + x(3 + x)) = 2
(6 + 2x + (3 * x + x * x)) = 2
(6 + 2x + (3x + x2)) = 2

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 2

Solving
6 + 5x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
6 + -2 + 5x + x2 = 2 + -2

Combine like terms: 6 + -2 = 4
4 + 5x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
4 + 5x + x2 = 0

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

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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

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