-3y(y+3)=2y+3

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

Simplifying
-3y(y + 3) = 2y + 3

Reorder the terms:
-3y(3 + y) = 2y + 3
(3 * -3y + y * -3y) = 2y + 3
(-9y + -3y2) = 2y + 3

Reorder the terms:
-9y + -3y2 = 3 + 2y

Solving
-9y + -3y2 = 3 + 2y

Solving for variable 'y'.

Reorder the terms:
-3 + -9y + -2y + -3y2 = 3 + 2y + -3 + -2y

Combine like terms: -9y + -2y = -11y
-3 + -11y + -3y2 = 3 + 2y + -3 + -2y

Reorder the terms:
-3 + -11y + -3y2 = 3 + -3 + 2y + -2y

Combine like terms: 3 + -3 = 0
-3 + -11y + -3y2 = 0 + 2y + -2y
-3 + -11y + -3y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-3 + -11y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 11y + 3y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 11y + 3y2)' equal to zero and attempt to solve:

Simplifying
3 + 11y + 3y2 = 0

Solving
3 + 11y + 3y2 = 0

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

Divide each side by '3'.
1 + 3.666666667y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3.666666667y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + 3.666666667y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3.666666667y + y2 = 0 + -1
3.666666667y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
3.666666667y + y2 = -1

The y term is 3.666666667y.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667y + 3.361111114 + y2 = -1 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667y + y2 = -1 + 3.361111114

Combine like terms: -1 + 3.361111114 = 2.361111114
3.361111114 + 3.666666667y + y2 = 2.361111114

Factor a perfect square on the left side:
(y + 1.833333334)(y + 1.833333334) = 2.361111114

Calculate the square root of the right side: 1.536590744

Break this problem into two subproblems by setting 
(y + 1.833333334) equal to 1.536590744 and -1.536590744.

Subproblem 1
y + 1.833333334 = 1.536590744

Simplifying
y + 1.833333334 = 1.536590744

Reorder the terms:
1.833333334 + y = 1.536590744

Solving
1.833333334 + y = 1.536590744

Solving for variable 'y'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + y = 1.536590744 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + y = 1.536590744 + -1.833333334
y = 1.536590744 + -1.833333334

Combine like terms: 1.536590744 + -1.833333334 = -0.29674259
y = -0.29674259

Simplifying
y = -0.29674259

Subproblem 2
y + 1.833333334 = -1.536590744

Simplifying
y + 1.833333334 = -1.536590744

Reorder the terms:
1.833333334 + y = -1.536590744

Solving
1.833333334 + y = -1.536590744

Solving for variable 'y'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + y = -1.536590744 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + y = -1.536590744 + -1.833333334
y = -1.536590744 + -1.833333334

Combine like terms: -1.536590744 + -1.833333334 = -3.369924078
y = -3.369924078

Simplifying
y = -3.369924078

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.29674259, -3.369924078}
Solution
y = {-0.29674259, -3.369924078}