(x+1)(x+1)=x+1

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

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

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

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

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

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

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

Add '-1' to each side of the equation.
1 + 2x + -1 + x2 = 1 + -1 + x

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

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

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

Solving
2x + x2 = x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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 = {0, -1}