3y-1=y^2+1

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

Simplifying
3y + -1 = y2 + 1

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

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

Solving
-1 + 3y = 1 + y2

Solving for variable 'y'.

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

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

Reorder the terms:
-2 + 3y + -1y2 = 1 + -1 + y2 + -1y2

Combine like terms: 1 + -1 = 0
-2 + 3y + -1y2 = 0 + y2 + -1y2
-2 + 3y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-2 + 3y + -1y2 = 0

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

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

Simplifying
-2 + y = 0

Solving
-2 + y = 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 + y = 0 + 2

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

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

Simplifying
y = 2
Subproblem 2
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
Solution
y = {2, 1}