-3y(3y+5)=-6(y+6)+3y

Solution for -3y(3y+5)=-6(y+6)+3y equation:

Simplifying
-3y(3y + 5) = -6(y + 6) + 3y

Reorder the terms:
-3y(5 + 3y) = -6(y + 6) + 3y
(5 * -3y + 3y * -3y) = -6(y + 6) + 3y
(-15y + -9y2) = -6(y + 6) + 3y

Reorder the terms:
-15y + -9y2 = -6(6 + y) + 3y
-15y + -9y2 = (6 * -6 + y * -6) + 3y
-15y + -9y2 = (-36 + -6y) + 3y

Combine like terms: -6y + 3y = -3y
-15y + -9y2 = -36 + -3y

Solving
-15y + -9y2 = -36 + -3y

Solving for variable 'y'.

Reorder the terms:
36 + -15y + 3y + -9y2 = -36 + -3y + 36 + 3y

Combine like terms: -15y + 3y = -12y
36 + -12y + -9y2 = -36 + -3y + 36 + 3y

Reorder the terms:
36 + -12y + -9y2 = -36 + 36 + -3y + 3y

Combine like terms: -36 + 36 = 0
36 + -12y + -9y2 = 0 + -3y + 3y
36 + -12y + -9y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
36 + -12y + -9y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -4y + -3y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(12 + -4y + -3y2)' equal to zero and attempt to solve:

Simplifying
12 + -4y + -3y2 = 0

Solving
12 + -4y + -3y2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-4 + 1.333333333y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.333333333y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.333333333y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.333333333y + y2 = 0 + 4
1.333333333y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.333333333y + y2 = 4

The y term is 1.333333333y.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333y + 0.4444444442 + y2 = 4 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333y + y2 = 4 + 0.4444444442

Combine like terms: 4 + 0.4444444442 = 4.4444444442
0.4444444442 + 1.333333333y + y2 = 4.4444444442

Factor a perfect square on the left side:
(y + 0.6666666665)(y + 0.6666666665) = 4.4444444442

Calculate the square root of the right side: 2.108185107

Break this problem into two subproblems by setting 
(y + 0.6666666665) equal to 2.108185107 and -2.108185107.

Subproblem 1
y + 0.6666666665 = 2.108185107

Simplifying
y + 0.6666666665 = 2.108185107

Reorder the terms:
0.6666666665 + y = 2.108185107

Solving
0.6666666665 + y = 2.108185107

Solving for variable 'y'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + y = 2.108185107 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + y = 2.108185107 + -0.6666666665
y = 2.108185107 + -0.6666666665

Combine like terms: 2.108185107 + -0.6666666665 = 1.4415184405
y = 1.4415184405

Simplifying
y = 1.4415184405

Subproblem 2
y + 0.6666666665 = -2.108185107

Simplifying
y + 0.6666666665 = -2.108185107

Reorder the terms:
0.6666666665 + y = -2.108185107

Solving
0.6666666665 + y = -2.108185107

Solving for variable 'y'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + y = -2.108185107 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + y = -2.108185107 + -0.6666666665
y = -2.108185107 + -0.6666666665

Combine like terms: -2.108185107 + -0.6666666665 = -2.7748517735
y = -2.7748517735

Simplifying
y = -2.7748517735

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.4415184405, -2.7748517735}
Solution
y = {1.4415184405, -2.7748517735}