u^2+2u=-1

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

Simplifying
u2 + 2u = -1

Reorder the terms:
2u + u2 = -1

Solving
2u + u2 = -1

Solving for variable 'u'.

Reorder the terms:
1 + 2u + u2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 2u + u2 = 0

Factor a trinomial.
(1 + u)(1 + u) = 0

Subproblem 1
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
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 = {-1, -1}