6y-6-8y=12y(y+3)-2

Solution for 6y-6-8y=12y(y+3)-2 equation:

Simplifying
6y + -6 + -8y = 12y(y + 3) + -2

Reorder the terms:
-6 + 6y + -8y = 12y(y + 3) + -2

Combine like terms: 6y + -8y = -2y
-6 + -2y = 12y(y + 3) + -2

Reorder the terms:
-6 + -2y = 12y(3 + y) + -2
-6 + -2y = (3 * 12y + y * 12y) + -2
-6 + -2y = (36y + 12y2) + -2

Reorder the terms:
-6 + -2y = -2 + 36y + 12y2

Solving
-6 + -2y = -2 + 36y + 12y2

Solving for variable 'y'.

Reorder the terms:
-6 + 2 + -2y + -36y + -12y2 = -2 + 36y + 12y2 + 2 + -36y + -12y2

Combine like terms: -6 + 2 = -4
-4 + -2y + -36y + -12y2 = -2 + 36y + 12y2 + 2 + -36y + -12y2

Combine like terms: -2y + -36y = -38y
-4 + -38y + -12y2 = -2 + 36y + 12y2 + 2 + -36y + -12y2

Reorder the terms:
-4 + -38y + -12y2 = -2 + 2 + 36y + -36y + 12y2 + -12y2

Combine like terms: -2 + 2 = 0
-4 + -38y + -12y2 = 0 + 36y + -36y + 12y2 + -12y2
-4 + -38y + -12y2 = 36y + -36y + 12y2 + -12y2

Combine like terms: 36y + -36y = 0
-4 + -38y + -12y2 = 0 + 12y2 + -12y2
-4 + -38y + -12y2 = 12y2 + -12y2

Combine like terms: 12y2 + -12y2 = 0
-4 + -38y + -12y2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(2 + 19y + 6y2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(2 + 19y + 6y2)' equal to zero and attempt to solve:

Simplifying
2 + 19y + 6y2 = 0

Solving
2 + 19y + 6y2 = 0

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

Divide each side by '6'.
0.3333333333 + 3.166666667y + y2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 3.166666667y + -0.3333333333 + y2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 3.166666667y + y2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 3.166666667y + y2 = 0 + -0.3333333333
3.166666667y + y2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
3.166666667y + y2 = -0.3333333333

The y term is 3.166666667y.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667y + 2.506944447 + y2 = -0.3333333333 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667y + y2 = -0.3333333333 + 2.506944447

Combine like terms: -0.3333333333 + 2.506944447 = 2.1736111137
2.506944447 + 3.166666667y + y2 = 2.1736111137

Factor a perfect square on the left side:
(y + 1.583333334)(y + 1.583333334) = 2.1736111137

Calculate the square root of the right side: 1.474317169

Break this problem into two subproblems by setting 
(y + 1.583333334) equal to 1.474317169 and -1.474317169.

Subproblem 1
y + 1.583333334 = 1.474317169

Simplifying
y + 1.583333334 = 1.474317169

Reorder the terms:
1.583333334 + y = 1.474317169

Solving
1.583333334 + y = 1.474317169

Solving for variable 'y'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + y = 1.474317169 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + y = 1.474317169 + -1.583333334
y = 1.474317169 + -1.583333334

Combine like terms: 1.474317169 + -1.583333334 = -0.109016165
y = -0.109016165

Simplifying
y = -0.109016165

Subproblem 2
y + 1.583333334 = -1.474317169

Simplifying
y + 1.583333334 = -1.474317169

Reorder the terms:
1.583333334 + y = -1.474317169

Solving
1.583333334 + y = -1.474317169

Solving for variable 'y'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + y = -1.474317169 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + y = -1.474317169 + -1.583333334
y = -1.474317169 + -1.583333334

Combine like terms: -1.474317169 + -1.583333334 = -3.057650503
y = -3.057650503

Simplifying
y = -3.057650503

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.109016165, -3.057650503}
Solution
y = {-0.109016165, -3.057650503}