5(y-7)8y=-20

Solution for 5(y-7)8y=-20 equation:

Simplifying
5(y + -7) * 8y = -20

Reorder the terms:
5(-7 + y) * 8y = -20

Reorder the terms for easier multiplication:
5 * 8y(-7 + y) = -20

Multiply 5 * 8
40y(-7 + y) = -20
(-7 * 40y + y * 40y) = -20
(-280y + 40y2) = -20

Solving
-280y + 40y2 = -20

Solving for variable 'y'.

Reorder the terms:
20 + -280y + 40y2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + -280y + 40y2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(1 + -14y + 2y2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(1 + -14y + 2y2)' equal to zero and attempt to solve:

Simplifying
1 + -14y + 2y2 = 0

Solving
1 + -14y + 2y2 = 0

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

Divide each side by '2'.
0.5 + -7y + y2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -7y + -0.5 + y2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -7y + y2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -7y + y2 = 0 + -0.5
-7y + y2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-7y + y2 = -0.5

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = -0.5 + 12.25

Reorder the terms:
12.25 + -7y + y2 = -0.5 + 12.25

Combine like terms: -0.5 + 12.25 = 11.75
12.25 + -7y + y2 = 11.75

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 11.75

Calculate the square root of the right side: 3.4278273

Break this problem into two subproblems by setting 
(y + -3.5) equal to 3.4278273 and -3.4278273.

Subproblem 1
y + -3.5 = 3.4278273

Simplifying
y + -3.5 = 3.4278273

Reorder the terms:
-3.5 + y = 3.4278273

Solving
-3.5 + y = 3.4278273

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = 3.4278273 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 3.4278273 + 3.5
y = 3.4278273 + 3.5

Combine like terms: 3.4278273 + 3.5 = 6.9278273
y = 6.9278273

Simplifying
y = 6.9278273

Subproblem 2
y + -3.5 = -3.4278273

Simplifying
y + -3.5 = -3.4278273

Reorder the terms:
-3.5 + y = -3.4278273

Solving
-3.5 + y = -3.4278273

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = -3.4278273 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -3.4278273 + 3.5
y = -3.4278273 + 3.5

Combine like terms: -3.4278273 + 3.5 = 0.0721727
y = 0.0721727

Simplifying
y = 0.0721727

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.9278273, 0.0721727}
Solution
y = {6.9278273, 0.0721727}