-8y(y+9)=-40

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Solution for -8y(y+9)=-40 equation: 


Simplifying
-8y(y + 9) = -40

Reorder the terms:
-8y(9 + y) = -40
(9 * -8y + y * -8y) = -40
(-72y + -8y2) = -40

Solving
-72y + -8y2 = -40

Solving for variable 'y'.

Reorder the terms:
40 + -72y + -8y2 = -40 + 40

Combine like terms: -40 + 40 = 0
40 + -72y + -8y2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + -9y + -1y2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(5 + -9y + -1y2)' equal to zero and attempt to solve:

Simplifying
5 + -9y + -1y2 = 0

Solving
5 + -9y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 9y + y2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 9y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + 9y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 9y + y2 = 0 + 5
9y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
9y + y2 = 5

The y term is 9y.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9y + 20.25 + y2 = 5 + 20.25

Reorder the terms:
20.25 + 9y + y2 = 5 + 20.25

Combine like terms: 5 + 20.25 = 25.25
20.25 + 9y + y2 = 25.25

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(y + 4.5) equal to 5.024937811 and -5.024937811.


Subproblem 1
y + 4.5 = 5.024937811

Simplifying
y + 4.5 = 5.024937811

Reorder the terms:
4.5 + y = 5.024937811

Solving
4.5 + y = 5.024937811

Solving for variable 'y'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = 5.024937811 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = 5.024937811 + -4.5
y = 5.024937811 + -4.5

Combine like terms: 5.024937811 + -4.5 = 0.524937811
y = 0.524937811

Simplifying
y = 0.524937811


Subproblem 2
y + 4.5 = -5.024937811

Simplifying
y + 4.5 = -5.024937811

Reorder the terms:
4.5 + y = -5.024937811

Solving
4.5 + y = -5.024937811

Solving for variable 'y'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = -5.024937811 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = -5.024937811 + -4.5
y = -5.024937811 + -4.5

Combine like terms: -5.024937811 + -4.5 = -9.524937811
y = -9.524937811

Simplifying
y = -9.524937811


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.524937811, -9.524937811}
Solution
y = {0.524937811, -9.524937811}

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