(y*y+2y)82=296

Solution for (y*y+2y)82=296 equation:

Simplifying
(y * y + 2y) * 82 = 296

Multiply y * y
(y2 + 2y) * 82 = 296

Reorder the terms:
(2y + y2) * 82 = 296

Reorder the terms for easier multiplication:
82(2y + y2) = 296
(2y * 82 + y2 * 82) = 296
(164y + 82y2) = 296

Solving
164y + 82y2 = 296

Solving for variable 'y'.

Reorder the terms:
-296 + 164y + 82y2 = 296 + -296

Combine like terms: 296 + -296 = 0
-296 + 164y + 82y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-148 + 82y + 41y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-148 + 82y + 41y2)' equal to zero and attempt to solve:

Simplifying
-148 + 82y + 41y2 = 0

Solving
-148 + 82y + 41y2 = 0

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

Divide each side by '41'.
-3.609756098 + 2y + y2 = 0

Move the constant term to the right:

Add '3.609756098' to each side of the equation.
-3.609756098 + 2y + 3.609756098 + y2 = 0 + 3.609756098

Reorder the terms:
-3.609756098 + 3.609756098 + 2y + y2 = 0 + 3.609756098

Combine like terms: -3.609756098 + 3.609756098 = 0.000000000
0.000000000 + 2y + y2 = 0 + 3.609756098
2y + y2 = 0 + 3.609756098

Combine like terms: 0 + 3.609756098 = 3.609756098
2y + y2 = 3.609756098

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 = 3.609756098 + 1

Reorder the terms:
1 + 2y + y2 = 3.609756098 + 1

Combine like terms: 3.609756098 + 1 = 4.609756098
1 + 2y + y2 = 4.609756098

Factor a perfect square on the left side:
(y + 1)(y + 1) = 4.609756098

Calculate the square root of the right side: 2.147034256

Break this problem into two subproblems by setting 
(y + 1) equal to 2.147034256 and -2.147034256.

Subproblem 1
y + 1 = 2.147034256

Simplifying
y + 1 = 2.147034256

Reorder the terms:
1 + y = 2.147034256

Solving
1 + y = 2.147034256

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 = 2.147034256 + -1

Combine like terms: 1 + -1 = 0
0 + y = 2.147034256 + -1
y = 2.147034256 + -1

Combine like terms: 2.147034256 + -1 = 1.147034256
y = 1.147034256

Simplifying
y = 1.147034256

Subproblem 2
y + 1 = -2.147034256

Simplifying
y + 1 = -2.147034256

Reorder the terms:
1 + y = -2.147034256

Solving
1 + y = -2.147034256

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 = -2.147034256 + -1

Combine like terms: 1 + -1 = 0
0 + y = -2.147034256 + -1
y = -2.147034256 + -1

Combine like terms: -2.147034256 + -1 = -3.147034256
y = -3.147034256

Simplifying
y = -3.147034256

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.147034256, -3.147034256}
Solution
y = {1.147034256, -3.147034256}