u^2+1+u-1=0

Solution for u^2+1+u-1=0 equation:

Simplifying
u2 + 1 + u + -1 = 0

Reorder the terms:
1 + -1 + u + u2 = 0

Combine like terms: 1 + -1 = 0
0 + u + u2 = 0
u + u2 = 0

Solving
u + u2 = 0

Solving for variable 'u'.

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

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

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(1 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

Solving
1 + u = 0

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

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

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

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

Simplifying
u = -1
Solution
u = {0, -1}