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

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

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

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

Reorder the terms for easier multiplication:
2y(2 + -2y) = -2
(2 * 2y + -2y * 2y) = -2
(4y + -4y2) = -2

Solving
4y + -4y2 = -2

Solving for variable 'y'.

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2y + -2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 2y + -2y2)' equal to zero and attempt to solve:

Simplifying
1 + 2y + -2y2 = 0

Solving
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}
Solution
y = {1.366025404, -0.366025404}