(8y+2)(25y-20)=180

Solution for (8y+2)(25y-20)=180 equation:

Simplifying
(8y + 2)(25y + -20) = 180

Reorder the terms:
(2 + 8y)(25y + -20) = 180

Reorder the terms:
(2 + 8y)(-20 + 25y) = 180

Multiply (2 + 8y) * (-20 + 25y)
(2(-20 + 25y) + 8y * (-20 + 25y)) = 180
((-20 * 2 + 25y * 2) + 8y * (-20 + 25y)) = 180
((-40 + 50y) + 8y * (-20 + 25y)) = 180
(-40 + 50y + (-20 * 8y + 25y * 8y)) = 180
(-40 + 50y + (-160y + 200y2)) = 180

Combine like terms: 50y + -160y = -110y
(-40 + -110y + 200y2) = 180

Solving
-40 + -110y + 200y2 = 180

Solving for variable 'y'.

Reorder the terms:
-40 + -180 + -110y + 200y2 = 180 + -180

Combine like terms: -40 + -180 = -220
-220 + -110y + 200y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-220 + -110y + 200y2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-22 + -11y + 20y2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-22 + -11y + 20y2)' equal to zero and attempt to solve:

Simplifying
-22 + -11y + 20y2 = 0

Solving
-22 + -11y + 20y2 = 0

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

Divide each side by '20'.
-1.1 + -0.55y + y2 = 0.0

Move the constant term to the right:

Add '1.1' to each side of the equation.
-1.1 + -0.55y + 1.1 + y2 = 0.0 + 1.1

Reorder the terms:
-1.1 + 1.1 + -0.55y + y2 = 0.0 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + -0.55y + y2 = 0.0 + 1.1
-0.55y + y2 = 0.0 + 1.1

Combine like terms: 0.0 + 1.1 = 1.1
-0.55y + y2 = 1.1

The y term is -0.55y.  Take half its coefficient (-0.275).
Square it (0.075625) and add it to both sides.

Add '0.075625' to each side of the equation.
-0.55y + 0.075625 + y2 = 1.1 + 0.075625

Reorder the terms:
0.075625 + -0.55y + y2 = 1.1 + 0.075625

Combine like terms: 1.1 + 0.075625 = 1.175625
0.075625 + -0.55y + y2 = 1.175625

Factor a perfect square on the left side:
(y + -0.275)(y + -0.275) = 1.175625

Calculate the square root of the right side: 1.084262422

Break this problem into two subproblems by setting 
(y + -0.275) equal to 1.084262422 and -1.084262422.

Subproblem 1
y + -0.275 = 1.084262422

Simplifying
y + -0.275 = 1.084262422

Reorder the terms:
-0.275 + y = 1.084262422

Solving
-0.275 + y = 1.084262422

Solving for variable 'y'.

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

Add '0.275' to each side of the equation.
-0.275 + 0.275 + y = 1.084262422 + 0.275

Combine like terms: -0.275 + 0.275 = 0.000
0.000 + y = 1.084262422 + 0.275
y = 1.084262422 + 0.275

Combine like terms: 1.084262422 + 0.275 = 1.359262422
y = 1.359262422

Simplifying
y = 1.359262422

Subproblem 2
y + -0.275 = -1.084262422

Simplifying
y + -0.275 = -1.084262422

Reorder the terms:
-0.275 + y = -1.084262422

Solving
-0.275 + y = -1.084262422

Solving for variable 'y'.

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

Add '0.275' to each side of the equation.
-0.275 + 0.275 + y = -1.084262422 + 0.275

Combine like terms: -0.275 + 0.275 = 0.000
0.000 + y = -1.084262422 + 0.275
y = -1.084262422 + 0.275

Combine like terms: -1.084262422 + 0.275 = -0.809262422
y = -0.809262422

Simplifying
y = -0.809262422

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.359262422, -0.809262422}
Solution
y = {1.359262422, -0.809262422}