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

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

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

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

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

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

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

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

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

Solving
1x + x2 = 2 + 2x

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-1 + -1x)(2 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

Divide each side by '-1'.
x = -1

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}