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

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

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

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

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

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

Remove parenthesis around (1 + y)
-1y + 2y2 = 1 + y

Solving
-1y + 2y2 = 1 + y

Solving for variable 'y'.

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

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

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

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

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

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + -1y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1y + y2 = 0 + 0.5
-1y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1y + y2 = 0.5

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 0.5 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
0.25 + -1y + y2 = 0.75

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(y + -0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
y + -0.5 = 0.866025404

Simplifying
y + -0.5 = 0.866025404

Reorder the terms:
-0.5 + y = 0.866025404

Solving
-0.5 + y = 0.866025404

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 0.866025404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 0.866025404 + 0.5
y = 0.866025404 + 0.5

Combine like terms: 0.866025404 + 0.5 = 1.366025404
y = 1.366025404

Simplifying
y = 1.366025404

Subproblem 2
y + -0.5 = -0.866025404

Simplifying
y + -0.5 = -0.866025404

Reorder the terms:
-0.5 + y = -0.866025404

Solving
-0.5 + y = -0.866025404

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -0.866025404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -0.866025404 + 0.5
y = -0.866025404 + 0.5

Combine like terms: -0.866025404 + 0.5 = -0.366025404
y = -0.366025404

Simplifying
y = -0.366025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.366025404, -0.366025404}