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

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

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

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

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

Combine like terms: 2y + 2y = 4y
-32 + 4y + y2 = 7 + -1[15y(2 + y)]
-32 + 4y + y2 = 7 + -1[(2 * 15y + y * 15y)]
-32 + 4y + y2 = 7 + -1[(30y + 15y2)]
-32 + 4y + y2 = 7 + [30y * -1 + 15y2 * -1]
-32 + 4y + y2 = 7 + [-30y + -15y2]

Solving
-32 + 4y + y2 = 7 + -30y + -15y2

Solving for variable 'y'.

Reorder the terms:
-32 + -7 + 4y + 30y + y2 + 15y2 = 7 + -30y + -15y2 + -7 + 30y + 15y2

Combine like terms: -32 + -7 = -39
-39 + 4y + 30y + y2 + 15y2 = 7 + -30y + -15y2 + -7 + 30y + 15y2

Combine like terms: 4y + 30y = 34y
-39 + 34y + y2 + 15y2 = 7 + -30y + -15y2 + -7 + 30y + 15y2

Combine like terms: y2 + 15y2 = 16y2
-39 + 34y + 16y2 = 7 + -30y + -15y2 + -7 + 30y + 15y2

Reorder the terms:
-39 + 34y + 16y2 = 7 + -7 + -30y + 30y + -15y2 + 15y2

Combine like terms: 7 + -7 = 0
-39 + 34y + 16y2 = 0 + -30y + 30y + -15y2 + 15y2
-39 + 34y + 16y2 = -30y + 30y + -15y2 + 15y2

Combine like terms: -30y + 30y = 0
-39 + 34y + 16y2 = 0 + -15y2 + 15y2
-39 + 34y + 16y2 = -15y2 + 15y2

Combine like terms: -15y2 + 15y2 = 0
-39 + 34y + 16y2 = 0

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

Divide each side by '16'.
-2.4375 + 2.125y + y2 = 0

Move the constant term to the right:

Add '2.4375' to each side of the equation.
-2.4375 + 2.125y + 2.4375 + y2 = 0 + 2.4375

Reorder the terms:
-2.4375 + 2.4375 + 2.125y + y2 = 0 + 2.4375

Combine like terms: -2.4375 + 2.4375 = 0.0000
0.0000 + 2.125y + y2 = 0 + 2.4375
2.125y + y2 = 0 + 2.4375

Combine like terms: 0 + 2.4375 = 2.4375
2.125y + y2 = 2.4375

The y term is 2.125y.  Take half its coefficient (1.0625).
Square it (1.12890625) and add it to both sides.

Add '1.12890625' to each side of the equation.
2.125y + 1.12890625 + y2 = 2.4375 + 1.12890625

Reorder the terms:
1.12890625 + 2.125y + y2 = 2.4375 + 1.12890625

Combine like terms: 2.4375 + 1.12890625 = 3.56640625
1.12890625 + 2.125y + y2 = 3.56640625

Factor a perfect square on the left side:
(y + 1.0625)(y + 1.0625) = 3.56640625

Calculate the square root of the right side: 1.888493116

Break this problem into two subproblems by setting 
(y + 1.0625) equal to 1.888493116 and -1.888493116.

Subproblem 1
y + 1.0625 = 1.888493116

Simplifying
y + 1.0625 = 1.888493116

Reorder the terms:
1.0625 + y = 1.888493116

Solving
1.0625 + y = 1.888493116

Solving for variable 'y'.

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

Add '-1.0625' to each side of the equation.
1.0625 + -1.0625 + y = 1.888493116 + -1.0625

Combine like terms: 1.0625 + -1.0625 = 0.0000
0.0000 + y = 1.888493116 + -1.0625
y = 1.888493116 + -1.0625

Combine like terms: 1.888493116 + -1.0625 = 0.825993116
y = 0.825993116

Simplifying
y = 0.825993116

Subproblem 2
y + 1.0625 = -1.888493116

Simplifying
y + 1.0625 = -1.888493116

Reorder the terms:
1.0625 + y = -1.888493116

Solving
1.0625 + y = -1.888493116

Solving for variable 'y'.

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

Add '-1.0625' to each side of the equation.
1.0625 + -1.0625 + y = -1.888493116 + -1.0625

Combine like terms: 1.0625 + -1.0625 = 0.0000
0.0000 + y = -1.888493116 + -1.0625
y = -1.888493116 + -1.0625

Combine like terms: -1.888493116 + -1.0625 = -2.950993116
y = -2.950993116

Simplifying
y = -2.950993116

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.825993116, -2.950993116}