-2y^2+6y=2

Solution for -2y^2+6y=2 equation:

Simplifying
-2y2 + 6y = 2

Reorder the terms:
6y + -2y2 = 2

Solving
6y + -2y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + 6y + -2y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 6y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 3y + -1y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 3y + -1y2)' equal to zero and attempt to solve:

Simplifying
-1 + 3y + -1y2 = 0

Solving
-1 + 3y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1 + -3y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -3y + y2 = 0 + -1

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

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

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -1 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3y + y2 = 1.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
y + -1.5 = 1.118033989

Simplifying
y + -1.5 = 1.118033989

Reorder the terms:
-1.5 + y = 1.118033989

Solving
-1.5 + y = 1.118033989

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.118033989 + 1.5
y = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
y = 2.618033989

Simplifying
y = 2.618033989

Subproblem 2
y + -1.5 = -1.118033989

Simplifying
y + -1.5 = -1.118033989

Reorder the terms:
-1.5 + y = -1.118033989

Solving
-1.5 + y = -1.118033989

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.118033989 + 1.5
y = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
y = 0.381966011

Simplifying
y = 0.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.618033989, 0.381966011}
Solution
y = {2.618033989, 0.381966011}