10y(8y+4)=180

Solution for 10y(8y+4)=180 equation:

Simplifying
10y(8y + 4) = 180

Reorder the terms:
10y(4 + 8y) = 180
(4 * 10y + 8y * 10y) = 180
(40y + 80y2) = 180

Solving
40y + 80y2 = 180

Solving for variable 'y'.

Reorder the terms:
-180 + 40y + 80y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 40y + 80y2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-9 + 2y + 4y2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-9 + 2y + 4y2)' equal to zero and attempt to solve:

Simplifying
-9 + 2y + 4y2 = 0

Solving
-9 + 2y + 4y2 = 0

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

Divide each side by '4'.
-2.25 + 0.5y + y2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.5y + 2.25 + y2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.5y + y2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.5y + y2 = 0 + 2.25
0.5y + y2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.5y + y2 = 2.25

The y term is 0.5y.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5y + 0.0625 + y2 = 2.25 + 0.0625

Reorder the terms:
0.0625 + 0.5y + y2 = 2.25 + 0.0625

Combine like terms: 2.25 + 0.0625 = 2.3125
0.0625 + 0.5y + y2 = 2.3125

Factor a perfect square on the left side:
(y + 0.25)(y + 0.25) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(y + 0.25) equal to 1.520690633 and -1.520690633.

Subproblem 1
y + 0.25 = 1.520690633

Simplifying
y + 0.25 = 1.520690633

Reorder the terms:
0.25 + y = 1.520690633

Solving
0.25 + y = 1.520690633

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = 1.520690633 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = 1.520690633 + -0.25
y = 1.520690633 + -0.25

Combine like terms: 1.520690633 + -0.25 = 1.270690633
y = 1.270690633

Simplifying
y = 1.270690633

Subproblem 2
y + 0.25 = -1.520690633

Simplifying
y + 0.25 = -1.520690633

Reorder the terms:
0.25 + y = -1.520690633

Solving
0.25 + y = -1.520690633

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = -1.520690633 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = -1.520690633 + -0.25
y = -1.520690633 + -0.25

Combine like terms: -1.520690633 + -0.25 = -1.770690633
y = -1.770690633

Simplifying
y = -1.770690633

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.270690633, -1.770690633}
Solution
y = {1.270690633, -1.770690633}