-3y^2-9y=1

Solution for -3y^2-9y=1 equation:

Simplifying
-3y2 + -9y = 1

Reorder the terms:
-9y + -3y2 = 1

Solving
-9y + -3y2 = 1

Solving for variable 'y'.

Reorder the terms:
-1 + -9y + -3y2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -9y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 9y + 3y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 9y + 3y2)' equal to zero and attempt to solve:

Simplifying
1 + 9y + 3y2 = 0

Solving
1 + 9y + 3y2 = 0

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

Divide each side by '3'.
0.3333333333 + 3y + y2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 3y + -0.3333333333 + y2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 3y + y2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 3y + y2 = 0 + -0.3333333333
3y + y2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
3y + y2 = -0.3333333333

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 = -0.3333333333 + 2.25

Reorder the terms:
2.25 + 3y + y2 = -0.3333333333 + 2.25

Combine like terms: -0.3333333333 + 2.25 = 1.9166666667
2.25 + 3y + y2 = 1.9166666667

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 1.9166666667

Calculate the square root of the right side: 1.38443731

Break this problem into two subproblems by setting 
(y + 1.5) equal to 1.38443731 and -1.38443731.

Subproblem 1
y + 1.5 = 1.38443731

Simplifying
y + 1.5 = 1.38443731

Reorder the terms:
1.5 + y = 1.38443731

Solving
1.5 + y = 1.38443731

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 = 1.38443731 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 1.38443731 + -1.5
y = 1.38443731 + -1.5

Combine like terms: 1.38443731 + -1.5 = -0.11556269
y = -0.11556269

Simplifying
y = -0.11556269

Subproblem 2
y + 1.5 = -1.38443731

Simplifying
y + 1.5 = -1.38443731

Reorder the terms:
1.5 + y = -1.38443731

Solving
1.5 + y = -1.38443731

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 = -1.38443731 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -1.38443731 + -1.5
y = -1.38443731 + -1.5

Combine like terms: -1.38443731 + -1.5 = -2.88443731
y = -2.88443731

Simplifying
y = -2.88443731

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.11556269, -2.88443731}
Solution
y = {-0.11556269, -2.88443731}