-5(2y+4)-6=-8(y+5)2y

Solution for -5(2y+4)-6=-8(y+5)2y equation:

Simplifying
-5(2y + 4) + -6 = -8(y + 5) * 2y

Reorder the terms:
-5(4 + 2y) + -6 = -8(y + 5) * 2y
(4 * -5 + 2y * -5) + -6 = -8(y + 5) * 2y
(-20 + -10y) + -6 = -8(y + 5) * 2y

Reorder the terms:
-20 + -6 + -10y = -8(y + 5) * 2y

Combine like terms: -20 + -6 = -26
-26 + -10y = -8(y + 5) * 2y

Reorder the terms:
-26 + -10y = -8(5 + y) * 2y

Reorder the terms for easier multiplication:
-26 + -10y = -8 * 2y(5 + y)

Multiply -8 * 2
-26 + -10y = -16y(5 + y)
-26 + -10y = (5 * -16y + y * -16y)
-26 + -10y = (-80y + -16y2)

Solving
-26 + -10y = -80y + -16y2

Solving for variable 'y'.

Combine like terms: -10y + 80y = 70y
-26 + 70y + 16y2 = -80y + -16y2 + 80y + 16y2

Reorder the terms:
-26 + 70y + 16y2 = -80y + 80y + -16y2 + 16y2

Combine like terms: -80y + 80y = 0
-26 + 70y + 16y2 = 0 + -16y2 + 16y2
-26 + 70y + 16y2 = -16y2 + 16y2

Combine like terms: -16y2 + 16y2 = 0
-26 + 70y + 16y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 35y + 8y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + 35y + 8y2)' equal to zero and attempt to solve:

Simplifying
-13 + 35y + 8y2 = 0

Solving
-13 + 35y + 8y2 = 0

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

Divide each side by '8'.
-1.625 + 4.375y + y2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + 4.375y + 1.625 + y2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + 4.375y + y2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + 4.375y + y2 = 0 + 1.625
4.375y + y2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
4.375y + y2 = 1.625

The y term is 4.375y.  Take half its coefficient (2.1875).
Square it (4.78515625) and add it to both sides.

Add '4.78515625' to each side of the equation.
4.375y + 4.78515625 + y2 = 1.625 + 4.78515625

Reorder the terms:
4.78515625 + 4.375y + y2 = 1.625 + 4.78515625

Combine like terms: 1.625 + 4.78515625 = 6.41015625
4.78515625 + 4.375y + y2 = 6.41015625

Factor a perfect square on the left side:
(y + 2.1875)(y + 2.1875) = 6.41015625

Calculate the square root of the right side: 2.531828638

Break this problem into two subproblems by setting 
(y + 2.1875) equal to 2.531828638 and -2.531828638.

Subproblem 1
y + 2.1875 = 2.531828638

Simplifying
y + 2.1875 = 2.531828638

Reorder the terms:
2.1875 + y = 2.531828638

Solving
2.1875 + y = 2.531828638

Solving for variable 'y'.

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

Add '-2.1875' to each side of the equation.
2.1875 + -2.1875 + y = 2.531828638 + -2.1875

Combine like terms: 2.1875 + -2.1875 = 0.0000
0.0000 + y = 2.531828638 + -2.1875
y = 2.531828638 + -2.1875

Combine like terms: 2.531828638 + -2.1875 = 0.344328638
y = 0.344328638

Simplifying
y = 0.344328638

Subproblem 2
y + 2.1875 = -2.531828638

Simplifying
y + 2.1875 = -2.531828638

Reorder the terms:
2.1875 + y = -2.531828638

Solving
2.1875 + y = -2.531828638

Solving for variable 'y'.

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

Add '-2.1875' to each side of the equation.
2.1875 + -2.1875 + y = -2.531828638 + -2.1875

Combine like terms: 2.1875 + -2.1875 = 0.0000
0.0000 + y = -2.531828638 + -2.1875
y = -2.531828638 + -2.1875

Combine like terms: -2.531828638 + -2.1875 = -4.719328638
y = -4.719328638

Simplifying
y = -4.719328638

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.344328638, -4.719328638}
Solution
y = {0.344328638, -4.719328638}