10y(4y+8)=20

Solution for 10y(4y+8)=20 equation:

Simplifying
10y(4y + 8) = 20

Reorder the terms:
10y(8 + 4y) = 20
(8 * 10y + 4y * 10y) = 20
(80y + 40y2) = 20

Solving
80y + 40y2 = 20

Solving for variable 'y'.

Reorder the terms:
-20 + 80y + 40y2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 80y + 40y2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-1 + 4y + 2y2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-1 + 4y + 2y2)' equal to zero and attempt to solve:

Simplifying
-1 + 4y + 2y2 = 0

Solving
-1 + 4y + 2y2 = 0

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

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

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2y + y2 = 0 + 0.5
2y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2y + y2 = 0.5

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 0.5 + 1

Reorder the terms:
1 + 2y + y2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + 2y + y2 = 1.5

Factor a perfect square on the left side:
(y + 1)(y + 1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(y + 1) equal to 1.224744871 and -1.224744871.

Subproblem 1
y + 1 = 1.224744871

Simplifying
y + 1 = 1.224744871

Reorder the terms:
1 + y = 1.224744871

Solving
1 + y = 1.224744871

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + y = 1.224744871 + -1
y = 1.224744871 + -1

Combine like terms: 1.224744871 + -1 = 0.224744871
y = 0.224744871

Simplifying
y = 0.224744871

Subproblem 2
y + 1 = -1.224744871

Simplifying
y + 1 = -1.224744871

Reorder the terms:
1 + y = -1.224744871

Solving
1 + y = -1.224744871

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + y = -1.224744871 + -1
y = -1.224744871 + -1

Combine like terms: -1.224744871 + -1 = -2.224744871
y = -2.224744871

Simplifying
y = -2.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.224744871, -2.224744871}
Solution
y = {0.224744871, -2.224744871}