6(8+-2y)5y=-8

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Solution for 6(8+-2y)5y=-8 equation: 


Simplifying
6(8 + -2y) * 5y = -8

Reorder the terms for easier multiplication:
6 * 5y(8 + -2y) = -8

Multiply 6 * 5
30y(8 + -2y) = -8
(8 * 30y + -2y * 30y) = -8
(240y + -60y2) = -8

Solving
240y + -60y2 = -8

Solving for variable 'y'.

Reorder the terms:
8 + 240y + -60y2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 240y + -60y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 60y + -15y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + 60y + -15y2)' equal to zero and attempt to solve:

Simplifying
2 + 60y + -15y2 = 0

Solving
2 + 60y + -15y2 = 0

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

Divide each side by '-15'.
-0.1333333333 + -4y + y2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + -4y + 0.1333333333 + y2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + -4y + y2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + -4y + y2 = 0 + 0.1333333333
-4y + y2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
-4y + y2 = 0.1333333333

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 0.1333333333 + 4

Reorder the terms:
4 + -4y + y2 = 0.1333333333 + 4

Combine like terms: 0.1333333333 + 4 = 4.1333333333
4 + -4y + y2 = 4.1333333333

Factor a perfect square on the left side:
(y + -2)(y + -2) = 4.1333333333

Calculate the square root of the right side: 2.033060091

Break this problem into two subproblems by setting 
(y + -2) equal to 2.033060091 and -2.033060091.


Subproblem 1
y + -2 = 2.033060091

Simplifying
y + -2 = 2.033060091

Reorder the terms:
-2 + y = 2.033060091

Solving
-2 + y = 2.033060091

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 2.033060091 + 2

Combine like terms: -2 + 2 = 0
0 + y = 2.033060091 + 2
y = 2.033060091 + 2

Combine like terms: 2.033060091 + 2 = 4.033060091
y = 4.033060091

Simplifying
y = 4.033060091


Subproblem 2
y + -2 = -2.033060091

Simplifying
y + -2 = -2.033060091

Reorder the terms:
-2 + y = -2.033060091

Solving
-2 + y = -2.033060091

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -2.033060091 + 2

Combine like terms: -2 + 2 = 0
0 + y = -2.033060091 + 2
y = -2.033060091 + 2

Combine like terms: -2.033060091 + 2 = -0.033060091
y = -0.033060091

Simplifying
y = -0.033060091


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.033060091, -0.033060091}
Solution
y = {4.033060091, -0.033060091}

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