6y-2=2y(y-1)

Solution for 6y-2=2y(y-1) equation:

Simplifying
6y + -2 = 2y(y + -1)

Reorder the terms:
-2 + 6y = 2y(y + -1)

Reorder the terms:
-2 + 6y = 2y(-1 + y)
-2 + 6y = (-1 * 2y + y * 2y)
-2 + 6y = (-2y + 2y2)

Solving
-2 + 6y = -2y + 2y2

Solving for variable 'y'.

Combine like terms: 6y + 2y = 8y
-2 + 8y + -2y2 = -2y + 2y2 + 2y + -2y2

Reorder the terms:
-2 + 8y + -2y2 = -2y + 2y + 2y2 + -2y2

Combine like terms: -2y + 2y = 0
-2 + 8y + -2y2 = 0 + 2y2 + -2y2
-2 + 8y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-2 + 8y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4y + -1y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 4y + -1y2)' equal to zero and attempt to solve:

Simplifying
-1 + 4y + -1y2 = 0

Solving
-1 + 4y + -1y2 = 0

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

Divide each side by '-1'.
1 + -4y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -4y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4y + y2 = 0 + -1
-4y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4y + y2 = -1

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = -1 + 4

Reorder the terms:
4 + -4y + y2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + -4y + y2 = 3

Factor a perfect square on the left side:
(y + -2)(y + -2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + -2) equal to 1.732050808 and -1.732050808.

Subproblem 1
y + -2 = 1.732050808

Simplifying
y + -2 = 1.732050808

Reorder the terms:
-2 + y = 1.732050808

Solving
-2 + y = 1.732050808

Solving for variable 'y'.

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 = 1.732050808 + 2

Combine like terms: -2 + 2 = 0
0 + y = 1.732050808 + 2
y = 1.732050808 + 2

Combine like terms: 1.732050808 + 2 = 3.732050808
y = 3.732050808

Simplifying
y = 3.732050808

Subproblem 2
y + -2 = -1.732050808

Simplifying
y + -2 = -1.732050808

Reorder the terms:
-2 + y = -1.732050808

Solving
-2 + y = -1.732050808

Solving for variable 'y'.

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 = -1.732050808 + 2

Combine like terms: -2 + 2 = 0
0 + y = -1.732050808 + 2
y = -1.732050808 + 2

Combine like terms: -1.732050808 + 2 = 0.267949192
y = 0.267949192

Simplifying
y = 0.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.732050808, 0.267949192}
Solution
y = {3.732050808, 0.267949192}