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

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

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

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

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

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

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

Reorder the terms:
6 + 5x + x2 = (3 + x)

Remove parenthesis around (3 + x)
6 + 5x + x2 = 3 + x

Solving
6 + 5x + x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
6 + -3 + 5x + -1x + x2 = 3 + x + -3 + -1x

Combine like terms: 6 + -3 = 3
3 + 5x + -1x + x2 = 3 + x + -3 + -1x

Combine like terms: 5x + -1x = 4x
3 + 4x + x2 = 3 + x + -3 + -1x

Reorder the terms:
3 + 4x + x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
3 + 4x + x2 = 0 + x + -1x
3 + 4x + x2 = x + -1x

Combine like terms: x + -1x = 0
3 + 4x + x2 = 0

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

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
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 = {-3, -1}