y^2+1=-2y

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

Simplifying
y2 + 1 = -2y

Reorder the terms:
1 + y2 = -2y

Solving
1 + y2 = -2y

Solving for variable 'y'.

Reorder the terms:
1 + 2y + y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
1 + 2y + y2 = 0

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

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Solution
y = {-1, -1}