(x+1)-(x^2+1)=0

Solution for (x+1)-(x^2+1)=0 equation:

Simplifying
(x + 1) + -1(x2 + 1) = 0

Reorder the terms:
(1 + x) + -1(x2 + 1) = 0

Remove parenthesis around (1 + x)
1 + x + -1(x2 + 1) = 0

Reorder the terms:
1 + x + -1(1 + x2) = 0
1 + x + (1 * -1 + x2 * -1) = 0
1 + x + (-1 + -1x2) = 0

Reorder the terms:
1 + -1 + x + -1x2 = 0

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

Solving
x + -1x2 = 0

Solving for variable 'x'.

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