8y(8+6y)=20

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Solution for 8y(8+6y)=20 equation: 


Simplifying
8y(8 + 6y) = 20
(8 * 8y + 6y * 8y) = 20
(64y + 48y2) = 20

Solving
64y + 48y2 = 20

Solving for variable 'y'.

Reorder the terms:
-20 + 64y + 48y2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 64y + 48y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 16y + 12y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + 16y + 12y2)' equal to zero and attempt to solve:

Simplifying
-5 + 16y + 12y2 = 0

Solving
-5 + 16y + 12y2 = 0

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

Divide each side by '12'.
-0.4166666667 + 1.333333333y + y2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 1.333333333y + 0.4166666667 + y2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + 1.333333333y + y2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + 1.333333333y + y2 = 0 + 0.4166666667
1.333333333y + y2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
1.333333333y + y2 = 0.4166666667

The y term is 1.333333333y.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333y + 0.4444444442 + y2 = 0.4166666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333y + y2 = 0.4166666667 + 0.4444444442

Combine like terms: 0.4166666667 + 0.4444444442 = 0.8611111109
0.4444444442 + 1.333333333y + y2 = 0.8611111109

Factor a perfect square on the left side:
(y + 0.6666666665)(y + 0.6666666665) = 0.8611111109

Calculate the square root of the right side: 0.927960727

Break this problem into two subproblems by setting 
(y + 0.6666666665) equal to 0.927960727 and -0.927960727.


Subproblem 1
y + 0.6666666665 = 0.927960727

Simplifying
y + 0.6666666665 = 0.927960727

Reorder the terms:
0.6666666665 + y = 0.927960727

Solving
0.6666666665 + y = 0.927960727

Solving for variable 'y'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + y = 0.927960727 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + y = 0.927960727 + -0.6666666665
y = 0.927960727 + -0.6666666665

Combine like terms: 0.927960727 + -0.6666666665 = 0.2612940605
y = 0.2612940605

Simplifying
y = 0.2612940605


Subproblem 2
y + 0.6666666665 = -0.927960727

Simplifying
y + 0.6666666665 = -0.927960727

Reorder the terms:
0.6666666665 + y = -0.927960727

Solving
0.6666666665 + y = -0.927960727

Solving for variable 'y'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + y = -0.927960727 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + y = -0.927960727 + -0.6666666665
y = -0.927960727 + -0.6666666665

Combine like terms: -0.927960727 + -0.6666666665 = -1.5946273935
y = -1.5946273935

Simplifying
y = -1.5946273935


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.2612940605, -1.5946273935}
Solution
y = {0.2612940605, -1.5946273935}

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