2(y-1)=y^2-1

Solution for 2(y-1)=y^2-1 equation:

Simplifying
2(y + -1) = y2 + -1

Reorder the terms:
2(-1 + y) = y2 + -1
(-1 * 2 + y * 2) = y2 + -1
(-2 + 2y) = y2 + -1

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

Solving
-2 + 2y = -1 + y2

Solving for variable 'y'.

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

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

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

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

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

Factor a trinomial.
(-1 + y)(1 + -1y) = 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 + -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 = {1, 1}