10-(2y-6)y=

Solution for 10-(2y-6)y= equation:

Simplifying
10 + -1(2y + -6) * y = 0

Reorder the terms:
10 + -1(-6 + 2y) * y = 0

Reorder the terms for easier multiplication:
10 + -1y(-6 + 2y) = 0
10 + (-6 * -1y + 2y * -1y) = 0
10 + (6y + -2y2) = 0

Solving
10 + 6y + -2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 3y + -1y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 3y + -1y2)' equal to zero and attempt to solve:

Simplifying
5 + 3y + -1y2 = 0

Solving
5 + 3y + -1y2 = 0

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

Divide each side by '-1'.
-5 + -3y + y2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + -3y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3y + y2 = 0 + 5
-3y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3y + y2 = 5

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 = 5 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3y + y2 = 7.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(y + -1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
y + -1.5 = 2.692582404

Simplifying
y + -1.5 = 2.692582404

Reorder the terms:
-1.5 + y = 2.692582404

Solving
-1.5 + y = 2.692582404

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 = 2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 2.692582404 + 1.5
y = 2.692582404 + 1.5

Combine like terms: 2.692582404 + 1.5 = 4.192582404
y = 4.192582404

Simplifying
y = 4.192582404

Subproblem 2
y + -1.5 = -2.692582404

Simplifying
y + -1.5 = -2.692582404

Reorder the terms:
-1.5 + y = -2.692582404

Solving
-1.5 + y = -2.692582404

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 = -2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -2.692582404 + 1.5
y = -2.692582404 + 1.5

Combine like terms: -2.692582404 + 1.5 = -1.192582404
y = -1.192582404

Simplifying
y = -1.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.192582404, -1.192582404}
Solution
y = {4.192582404, -1.192582404}