y(y+2)-2(16-y)=7-15-y(2+y)

Solution for y(y+2)-2(16-y)=7-15-y(2+y) equation:

Simplifying
y(y + 2) + -2(16 + -1y) = 7 + -15 + -1y(2 + y)

Reorder the terms:
y(2 + y) + -2(16 + -1y) = 7 + -15 + -1y(2 + y)
(2 * y + y * y) + -2(16 + -1y) = 7 + -15 + -1y(2 + y)
(2y + y2) + -2(16 + -1y) = 7 + -15 + -1y(2 + y)
2y + y2 + (16 * -2 + -1y * -2) = 7 + -15 + -1y(2 + y)
2y + y2 + (-32 + 2y) = 7 + -15 + -1y(2 + y)

Reorder the terms:
-32 + 2y + 2y + y2 = 7 + -15 + -1y(2 + y)

Combine like terms: 2y + 2y = 4y
-32 + 4y + y2 = 7 + -15 + -1y(2 + y)
-32 + 4y + y2 = 7 + -15 + (2 * -1y + y * -1y)
-32 + 4y + y2 = 7 + -15 + (-2y + -1y2)

Combine like terms: 7 + -15 = -8
-32 + 4y + y2 = -8 + -2y + -1y2

Solving
-32 + 4y + y2 = -8 + -2y + -1y2

Solving for variable 'y'.

Reorder the terms:
-32 + 8 + 4y + 2y + y2 + y2 = -8 + -2y + -1y2 + 8 + 2y + y2

Combine like terms: -32 + 8 = -24
-24 + 4y + 2y + y2 + y2 = -8 + -2y + -1y2 + 8 + 2y + y2

Combine like terms: 4y + 2y = 6y
-24 + 6y + y2 + y2 = -8 + -2y + -1y2 + 8 + 2y + y2

Combine like terms: y2 + y2 = 2y2
-24 + 6y + 2y2 = -8 + -2y + -1y2 + 8 + 2y + y2

Reorder the terms:
-24 + 6y + 2y2 = -8 + 8 + -2y + 2y + -1y2 + y2

Combine like terms: -8 + 8 = 0
-24 + 6y + 2y2 = 0 + -2y + 2y + -1y2 + y2
-24 + 6y + 2y2 = -2y + 2y + -1y2 + y2

Combine like terms: -2y + 2y = 0
-24 + 6y + 2y2 = 0 + -1y2 + y2
-24 + 6y + 2y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-24 + 6y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 3y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + 3y + y2)' equal to zero and attempt to solve:

Simplifying
-12 + 3y + y2 = 0

Solving
-12 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 3y + 12 + y2 = 0 + 12

Reorder the terms:
-12 + 12 + 3y + y2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 3y + y2 = 0 + 12
3y + y2 = 0 + 12

Combine like terms: 0 + 12 = 12
3y + y2 = 12

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 12 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + 3y + y2 = 14.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(y + 1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
y + 1.5 = 3.774917218

Simplifying
y + 1.5 = 3.774917218

Reorder the terms:
1.5 + y = 3.774917218

Solving
1.5 + y = 3.774917218

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 3.774917218 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 3.774917218 + -1.5
y = 3.774917218 + -1.5

Combine like terms: 3.774917218 + -1.5 = 2.274917218
y = 2.274917218

Simplifying
y = 2.274917218

Subproblem 2
y + 1.5 = -3.774917218

Simplifying
y + 1.5 = -3.774917218

Reorder the terms:
1.5 + y = -3.774917218

Solving
1.5 + y = -3.774917218

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -3.774917218 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -3.774917218 + -1.5
y = -3.774917218 + -1.5

Combine like terms: -3.774917218 + -1.5 = -5.274917218
y = -5.274917218

Simplifying
y = -5.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.274917218, -5.274917218}
Solution
y = {2.274917218, -5.274917218}