6(y+3)2y=26

Solution for 6(y+3)2y=26 equation:

Simplifying
6(y + 3) * 2y = 26

Reorder the terms:
6(3 + y) * 2y = 26

Reorder the terms for easier multiplication:
6 * 2y(3 + y) = 26

Multiply 6 * 2
12y(3 + y) = 26
(3 * 12y + y * 12y) = 26
(36y + 12y2) = 26

Solving
36y + 12y2 = 26

Solving for variable 'y'.

Reorder the terms:
-26 + 36y + 12y2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 36y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 18y + 6y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + 18y + 6y2)' equal to zero and attempt to solve:

Simplifying
-13 + 18y + 6y2 = 0

Solving
-13 + 18y + 6y2 = 0

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

Divide each side by '6'.
-2.166666667 + 3y + y2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + 3y + 2.166666667 + y2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + 3y + y2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + 3y + y2 = 0 + 2.166666667
3y + y2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
3y + y2 = 2.166666667

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 = 2.166666667 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 2.166666667 + 2.25

Combine like terms: 2.166666667 + 2.25 = 4.416666667
2.25 + 3y + y2 = 4.416666667

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 4.416666667

Calculate the square root of the right side: 2.101586702

Break this problem into two subproblems by setting 
(y + 1.5) equal to 2.101586702 and -2.101586702.

Subproblem 1
y + 1.5 = 2.101586702

Simplifying
y + 1.5 = 2.101586702

Reorder the terms:
1.5 + y = 2.101586702

Solving
1.5 + y = 2.101586702

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 = 2.101586702 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 2.101586702 + -1.5
y = 2.101586702 + -1.5

Combine like terms: 2.101586702 + -1.5 = 0.601586702
y = 0.601586702

Simplifying
y = 0.601586702

Subproblem 2
y + 1.5 = -2.101586702

Simplifying
y + 1.5 = -2.101586702

Reorder the terms:
1.5 + y = -2.101586702

Solving
1.5 + y = -2.101586702

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 = -2.101586702 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -2.101586702 + -1.5
y = -2.101586702 + -1.5

Combine like terms: -2.101586702 + -1.5 = -3.601586702
y = -3.601586702

Simplifying
y = -3.601586702

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.601586702, -3.601586702}
Solution
y = {0.601586702, -3.601586702}