y^2+1=2y+4

Solution for y^2+1=2y+4 equation:

Simplifying
y2 + 1 = 2y + 4

Reorder the terms:
1 + y2 = 2y + 4

Reorder the terms:
1 + y2 = 4 + 2y

Solving
1 + y2 = 4 + 2y

Solving for variable 'y'.

Reorder the terms:
1 + -4 + -2y + y2 = 4 + 2y + -4 + -2y

Combine like terms: 1 + -4 = -3
-3 + -2y + y2 = 4 + 2y + -4 + -2y

Reorder the terms:
-3 + -2y + y2 = 4 + -4 + 2y + -2y

Combine like terms: 4 + -4 = 0
-3 + -2y + y2 = 0 + 2y + -2y
-3 + -2y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-3 + -2y + y2 = 0

Factor a trinomial.
(-1 + -1y)(3 + -1y) = 0

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 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 + -1y = 0 + 1

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

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-1, 3}