y+3=y^2+1

Solution for y+3=y^2+1 equation:

Simplifying
y + 3 = y2 + 1

Reorder the terms:
3 + y = y2 + 1

Reorder the terms:
3 + y = 1 + y2

Solving
3 + y = 1 + y2

Solving for variable 'y'.

Reorder the terms:
3 + -1 + y + -1y2 = 1 + y2 + -1 + -1y2

Combine like terms: 3 + -1 = 2
2 + y + -1y2 = 1 + y2 + -1 + -1y2

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

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

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

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

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

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

Simplifying
y = 2
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 = {2, -1}