8y+((2y)(2y))=286

Solution for 8y+((2y)(2y))=286 equation:

Simplifying
8y + ((2y)(2y)) = 286

Remove parenthesis around (2y)
8y + (2y(2y)) = 286

Remove parenthesis around (2y)
8y + (2y * 2y) = 286

Reorder the terms for easier multiplication:
8y + (2 * 2y * y) = 286

Multiply 2 * 2
8y + (4y * y) = 286

Multiply y * y
8y + (4y2) = 286

Solving
8y + (4y2) = 286

Solving for variable 'y'.

Reorder the terms:
-286 + 8y + (4y2) = 286 + -286

Combine like terms: 286 + -286 = 0
-286 + 8y + (4y2) = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-143 + 4y + (2y2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-143 + 4y + (2y2))' equal to zero and attempt to solve:

Simplifying
-143 + 4y + (2y2) = 0

Solving
-143 + 4y + (2y2) = 0

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

Divide each side by '2'.
-71.5 + 2y + y2 = 0

Move the constant term to the right:

Add '71.5' to each side of the equation.
-71.5 + 2y + 71.5 + y2 = 0 + 71.5

Reorder the terms:
-71.5 + 71.5 + 2y + y2 = 0 + 71.5

Combine like terms: -71.5 + 71.5 = 0.0
0.0 + 2y + y2 = 0 + 71.5
2y + y2 = 0 + 71.5

Combine like terms: 0 + 71.5 = 71.5
2y + y2 = 71.5

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 = 71.5 + 1

Reorder the terms:
1 + 2y + y2 = 71.5 + 1

Combine like terms: 71.5 + 1 = 72.5
1 + 2y + y2 = 72.5

Factor a perfect square on the left side:
((y) + 1)((y) + 1) = 72.5

Calculate the square root of the right side: 8.514693183

Break this problem into two subproblems by setting 
((y) + 1) equal to 8.514693183 and -8.514693183.

Subproblem 1
(y) + 1 = 8.514693183

Simplifying
(y) + 1 = 8.514693183
y + 1 = 8.514693183

Reorder the terms:
1 + y = 8.514693183

Solving
1 + y = 8.514693183

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 = 8.514693183 + -1

Combine like terms: 1 + -1 = 0
0 + y = 8.514693183 + -1
y = 8.514693183 + -1

Combine like terms: 8.514693183 + -1 = 7.514693183
y = 7.514693183

Simplifying
y = 7.514693183

Subproblem 2
(y) + 1 = -8.514693183

Simplifying
(y) + 1 = -8.514693183
y + 1 = -8.514693183

Reorder the terms:
1 + y = -8.514693183

Solving
1 + y = -8.514693183

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 = -8.514693183 + -1

Combine like terms: 1 + -1 = 0
0 + y = -8.514693183 + -1
y = -8.514693183 + -1

Combine like terms: -8.514693183 + -1 = -9.514693183
y = -9.514693183

Simplifying
y = -9.514693183

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.514693183, -9.514693183}
Solution
y = {7.514693183, -9.514693183}