-5-5y(-6-2y)=0

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Solution for -5-5y(-6-2y)=0 equation: 


Simplifying
-5 + -5y(-6 + -2y) = 0
-5 + (-6 * -5y + -2y * -5y) = 0
-5 + (30y + 10y2) = 0

Solving
-5 + 30y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 6y + 2y2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-1 + 6y + 2y2)' equal to zero and attempt to solve:

Simplifying
-1 + 6y + 2y2 = 0

Solving
-1 + 6y + 2y2 = 0

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

Divide each side by '2'.
-0.5 + 3y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3y + y2 = 0 + 0.5
3y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3y + y2 = 0.5

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 = 0.5 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + 3y + y2 = 2.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(y + 1.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
y + 1.5 = 1.658312395

Simplifying
y + 1.5 = 1.658312395

Reorder the terms:
1.5 + y = 1.658312395

Solving
1.5 + y = 1.658312395

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 = 1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 1.658312395 + -1.5
y = 1.658312395 + -1.5

Combine like terms: 1.658312395 + -1.5 = 0.158312395
y = 0.158312395

Simplifying
y = 0.158312395


Subproblem 2
y + 1.5 = -1.658312395

Simplifying
y + 1.5 = -1.658312395

Reorder the terms:
1.5 + y = -1.658312395

Solving
1.5 + y = -1.658312395

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 = -1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -1.658312395 + -1.5
y = -1.658312395 + -1.5

Combine like terms: -1.658312395 + -1.5 = -3.158312395
y = -3.158312395

Simplifying
y = -3.158312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.158312395, -3.158312395}
Solution
y = {0.158312395, -3.158312395}

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