4y^2+64y+1024=880

Solution for 4y^2+64y+1024=880 equation:

Simplifying
4y2 + 64y + 1024 = 880

Reorder the terms:
1024 + 64y + 4y2 = 880

Solving
1024 + 64y + 4y2 = 880

Solving for variable 'y'.

Reorder the terms:
1024 + -880 + 64y + 4y2 = 880 + -880

Combine like terms: 1024 + -880 = 144
144 + 64y + 4y2 = 880 + -880

Combine like terms: 880 + -880 = 0
144 + 64y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + 16y + y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(36 + 16y + y2)' equal to zero and attempt to solve:

Simplifying
36 + 16y + y2 = 0

Solving
36 + 16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 16y + -36 + y2 = 0 + -36

Reorder the terms:
36 + -36 + 16y + y2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 16y + y2 = 0 + -36
16y + y2 = 0 + -36

Combine like terms: 0 + -36 = -36
16y + y2 = -36

The y term is 16y.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16y + 64 + y2 = -36 + 64

Reorder the terms:
64 + 16y + y2 = -36 + 64

Combine like terms: -36 + 64 = 28
64 + 16y + y2 = 28

Factor a perfect square on the left side:
(y + 8)(y + 8) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(y + 8) equal to 5.291502622 and -5.291502622.

Subproblem 1
y + 8 = 5.291502622

Simplifying
y + 8 = 5.291502622

Reorder the terms:
8 + y = 5.291502622

Solving
8 + y = 5.291502622

Solving for variable 'y'.

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

Add '-8' to each side of the equation.
8 + -8 + y = 5.291502622 + -8

Combine like terms: 8 + -8 = 0
0 + y = 5.291502622 + -8
y = 5.291502622 + -8

Combine like terms: 5.291502622 + -8 = -2.708497378
y = -2.708497378

Simplifying
y = -2.708497378

Subproblem 2
y + 8 = -5.291502622

Simplifying
y + 8 = -5.291502622

Reorder the terms:
8 + y = -5.291502622

Solving
8 + y = -5.291502622

Solving for variable 'y'.

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

Add '-8' to each side of the equation.
8 + -8 + y = -5.291502622 + -8

Combine like terms: 8 + -8 = 0
0 + y = -5.291502622 + -8
y = -5.291502622 + -8

Combine like terms: -5.291502622 + -8 = -13.291502622
y = -13.291502622

Simplifying
y = -13.291502622

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.708497378, -13.291502622}
Solution
y = {-2.708497378, -13.291502622}