-3y^2+6y+9=-2

Solution for -3y^2+6y+9=-2 equation:

Simplifying
-3y2 + 6y + 9 = -2

Reorder the terms:
9 + 6y + -3y2 = -2

Solving
9 + 6y + -3y2 = -2

Solving for variable 'y'.

Reorder the terms:
9 + 2 + 6y + -3y2 = -2 + 2

Combine like terms: 9 + 2 = 11
11 + 6y + -3y2 = -2 + 2

Combine like terms: -2 + 2 = 0
11 + 6y + -3y2 = 0

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

Divide each side by '-3'.
-3.666666667 + -2y + y2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -2y + 3.666666667 + y2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -2y + y2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -2y + y2 = 0 + 3.666666667
-2y + y2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-2y + y2 = 3.666666667

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 3.666666667 + 1

Reorder the terms:
1 + -2y + y2 = 3.666666667 + 1

Combine like terms: 3.666666667 + 1 = 4.666666667
1 + -2y + y2 = 4.666666667

Factor a perfect square on the left side:
(y + -1)(y + -1) = 4.666666667

Calculate the square root of the right side: 2.1602469

Break this problem into two subproblems by setting 
(y + -1) equal to 2.1602469 and -2.1602469.

Subproblem 1
y + -1 = 2.1602469

Simplifying
y + -1 = 2.1602469

Reorder the terms:
-1 + y = 2.1602469

Solving
-1 + y = 2.1602469

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 2.1602469 + 1

Combine like terms: -1 + 1 = 0
0 + y = 2.1602469 + 1
y = 2.1602469 + 1

Combine like terms: 2.1602469 + 1 = 3.1602469
y = 3.1602469

Simplifying
y = 3.1602469

Subproblem 2
y + -1 = -2.1602469

Simplifying
y + -1 = -2.1602469

Reorder the terms:
-1 + y = -2.1602469

Solving
-1 + y = -2.1602469

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -2.1602469 + 1

Combine like terms: -1 + 1 = 0
0 + y = -2.1602469 + 1
y = -2.1602469 + 1

Combine like terms: -2.1602469 + 1 = -1.1602469
y = -1.1602469

Simplifying
y = -1.1602469

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.1602469, -1.1602469}