28y^2+40y-80=-32y-64

Solution for 28y^2+40y-80=-32y-64 equation:

Simplifying
28y2 + 40y + -80 = -32y + -64

Reorder the terms:
-80 + 40y + 28y2 = -32y + -64

Reorder the terms:
-80 + 40y + 28y2 = -64 + -32y

Solving
-80 + 40y + 28y2 = -64 + -32y

Solving for variable 'y'.

Reorder the terms:
-80 + 64 + 40y + 32y + 28y2 = -64 + -32y + 64 + 32y

Combine like terms: -80 + 64 = -16
-16 + 40y + 32y + 28y2 = -64 + -32y + 64 + 32y

Combine like terms: 40y + 32y = 72y
-16 + 72y + 28y2 = -64 + -32y + 64 + 32y

Reorder the terms:
-16 + 72y + 28y2 = -64 + 64 + -32y + 32y

Combine like terms: -64 + 64 = 0
-16 + 72y + 28y2 = 0 + -32y + 32y
-16 + 72y + 28y2 = -32y + 32y

Combine like terms: -32y + 32y = 0
-16 + 72y + 28y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 18y + 7y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + 18y + 7y2)' equal to zero and attempt to solve:

Simplifying
-4 + 18y + 7y2 = 0

Solving
-4 + 18y + 7y2 = 0

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

Divide each side by '7'.
-0.5714285714 + 2.571428571y + y2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 2.571428571y + 0.5714285714 + y2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 2.571428571y + y2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 2.571428571y + y2 = 0 + 0.5714285714
2.571428571y + y2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
2.571428571y + y2 = 0.5714285714

The y term is 2.571428571y.  Take half its coefficient (1.285714286).
Square it (1.653061225) and add it to both sides.

Add '1.653061225' to each side of the equation.
2.571428571y + 1.653061225 + y2 = 0.5714285714 + 1.653061225

Reorder the terms:
1.653061225 + 2.571428571y + y2 = 0.5714285714 + 1.653061225

Combine like terms: 0.5714285714 + 1.653061225 = 2.2244897964
1.653061225 + 2.571428571y + y2 = 2.2244897964

Factor a perfect square on the left side:
(y + 1.285714286)(y + 1.285714286) = 2.2244897964

Calculate the square root of the right side: 1.491472359

Break this problem into two subproblems by setting 
(y + 1.285714286) equal to 1.491472359 and -1.491472359.

Subproblem 1
y + 1.285714286 = 1.491472359

Simplifying
y + 1.285714286 = 1.491472359

Reorder the terms:
1.285714286 + y = 1.491472359

Solving
1.285714286 + y = 1.491472359

Solving for variable 'y'.

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

Add '-1.285714286' to each side of the equation.
1.285714286 + -1.285714286 + y = 1.491472359 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + y = 1.491472359 + -1.285714286
y = 1.491472359 + -1.285714286

Combine like terms: 1.491472359 + -1.285714286 = 0.205758073
y = 0.205758073

Simplifying
y = 0.205758073

Subproblem 2
y + 1.285714286 = -1.491472359

Simplifying
y + 1.285714286 = -1.491472359

Reorder the terms:
1.285714286 + y = -1.491472359

Solving
1.285714286 + y = -1.491472359

Solving for variable 'y'.

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

Add '-1.285714286' to each side of the equation.
1.285714286 + -1.285714286 + y = -1.491472359 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + y = -1.491472359 + -1.285714286
y = -1.491472359 + -1.285714286

Combine like terms: -1.491472359 + -1.285714286 = -2.777186645
y = -2.777186645

Simplifying
y = -2.777186645

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.205758073, -2.777186645}
Solution
y = {0.205758073, -2.777186645}