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

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

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

Reorder the terms:
x(1 + x) + 1 = x + (x + 1)
(1 * x + x * x) + 1 = x + (x + 1)
(1x + x2) + 1 = x + (x + 1)

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

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

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

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

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

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

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

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

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

Solving
1x + x2 = 2x

Solving for variable 'x'.

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

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

Combine like terms: 2x + -2x = 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}