5y(-9-3y)=13

Solution for 5y(-9-3y)=13 equation:

Simplifying
5y(-9 + -3y) = 13
(-9 * 5y + -3y * 5y) = 13
(-45y + -15y2) = 13

Solving
-45y + -15y2 = 13

Solving for variable 'y'.

Reorder the terms:
-13 + -45y + -15y2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -45y + -15y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(13 + 45y + 15y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(13 + 45y + 15y2)' equal to zero and attempt to solve:

Simplifying
13 + 45y + 15y2 = 0

Solving
13 + 45y + 15y2 = 0

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

Divide each side by '15'.
0.8666666667 + 3y + y2 = 0

Move the constant term to the right:

Add '-0.8666666667' to each side of the equation.
0.8666666667 + 3y + -0.8666666667 + y2 = 0 + -0.8666666667

Reorder the terms:
0.8666666667 + -0.8666666667 + 3y + y2 = 0 + -0.8666666667

Combine like terms: 0.8666666667 + -0.8666666667 = 0.0000000000
0.0000000000 + 3y + y2 = 0 + -0.8666666667
3y + y2 = 0 + -0.8666666667

Combine like terms: 0 + -0.8666666667 = -0.8666666667
3y + y2 = -0.8666666667

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 = -0.8666666667 + 2.25

Reorder the terms:
2.25 + 3y + y2 = -0.8666666667 + 2.25

Combine like terms: -0.8666666667 + 2.25 = 1.3833333333
2.25 + 3y + y2 = 1.3833333333

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 1.3833333333

Calculate the square root of the right side: 1.176151918

Break this problem into two subproblems by setting 
(y + 1.5) equal to 1.176151918 and -1.176151918.

Subproblem 1
y + 1.5 = 1.176151918

Simplifying
y + 1.5 = 1.176151918

Reorder the terms:
1.5 + y = 1.176151918

Solving
1.5 + y = 1.176151918

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 = 1.176151918 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 1.176151918 + -1.5
y = 1.176151918 + -1.5

Combine like terms: 1.176151918 + -1.5 = -0.323848082
y = -0.323848082

Simplifying
y = -0.323848082

Subproblem 2
y + 1.5 = -1.176151918

Simplifying
y + 1.5 = -1.176151918

Reorder the terms:
1.5 + y = -1.176151918

Solving
1.5 + y = -1.176151918

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 = -1.176151918 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -1.176151918 + -1.5
y = -1.176151918 + -1.5

Combine like terms: -1.176151918 + -1.5 = -2.676151918
y = -2.676151918

Simplifying
y = -2.676151918

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.323848082, -2.676151918}
Solution
y = {-0.323848082, -2.676151918}