(x+2)*(x+1)=(x+1)

Solution for (x+2)*(x+1)=(x+1) equation:

Simplifying
(x + 2)(x + 1) = (x + 1)

Reorder the terms:
(2 + x)(x + 1) = (x + 1)

Reorder the terms:
(2 + x)(1 + x) = (x + 1)

Multiply (2 + x) * (1 + x)
(2(1 + x) + x(1 + x)) = (x + 1)
((1 * 2 + x * 2) + x(1 + x)) = (x + 1)
((2 + 2x) + x(1 + x)) = (x + 1)
(2 + 2x + (1 * x + x * x)) = (x + 1)
(2 + 2x + (1x + x2)) = (x + 1)

Combine like terms: 2x + 1x = 3x
(2 + 3x + x2) = (x + 1)

Reorder the terms:
2 + 3x + x2 = (1 + x)

Remove parenthesis around (1 + x)
2 + 3x + x2 = 1 + x

Solving
2 + 3x + x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
2 + -1 + 3x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: 2 + -1 = 1
1 + 3x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: 3x + -1x = 2x
1 + 2x + x2 = 1 + x + -1 + -1x

Reorder the terms:
1 + 2x + x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
1 + 2x + x2 = 0 + x + -1x
1 + 2x + x2 = x + -1x

Combine like terms: x + -1x = 0
1 + 2x + x2 = 0

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

Subproblem 1
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
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 = {-1, -1}