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

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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)]
-32 + 4y + y2 = [15 * 7 + -2y * 7 + -1y2 * 7]
-32 + 4y + y2 = [105 + -14y + -7y2]

Solving
-32 + 4y + y2 = 105 + -14y + -7y2

Solving for variable 'y'.

Reorder the terms:
-32 + -105 + 4y + 14y + y2 + 7y2 = 105 + -14y + -7y2 + -105 + 14y + 7y2

Combine like terms: -32 + -105 = -137
-137 + 4y + 14y + y2 + 7y2 = 105 + -14y + -7y2 + -105 + 14y + 7y2

Combine like terms: 4y + 14y = 18y
-137 + 18y + y2 + 7y2 = 105 + -14y + -7y2 + -105 + 14y + 7y2

Combine like terms: y2 + 7y2 = 8y2
-137 + 18y + 8y2 = 105 + -14y + -7y2 + -105 + 14y + 7y2

Reorder the terms:
-137 + 18y + 8y2 = 105 + -105 + -14y + 14y + -7y2 + 7y2

Combine like terms: 105 + -105 = 0
-137 + 18y + 8y2 = 0 + -14y + 14y + -7y2 + 7y2
-137 + 18y + 8y2 = -14y + 14y + -7y2 + 7y2

Combine like terms: -14y + 14y = 0
-137 + 18y + 8y2 = 0 + -7y2 + 7y2
-137 + 18y + 8y2 = -7y2 + 7y2

Combine like terms: -7y2 + 7y2 = 0
-137 + 18y + 8y2 = 0

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

Divide each side by '8'.
-17.125 + 2.25y + y2 = 0

Move the constant term to the right:

Add '17.125' to each side of the equation.
-17.125 + 2.25y + 17.125 + y2 = 0 + 17.125

Reorder the terms:
-17.125 + 17.125 + 2.25y + y2 = 0 + 17.125

Combine like terms: -17.125 + 17.125 = 0.000
0.000 + 2.25y + y2 = 0 + 17.125
2.25y + y2 = 0 + 17.125

Combine like terms: 0 + 17.125 = 17.125
2.25y + y2 = 17.125

The y term is 2.25y.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25y + 1.265625 + y2 = 17.125 + 1.265625

Reorder the terms:
1.265625 + 2.25y + y2 = 17.125 + 1.265625

Combine like terms: 17.125 + 1.265625 = 18.390625
1.265625 + 2.25y + y2 = 18.390625

Factor a perfect square on the left side:
(y + 1.125)(y + 1.125) = 18.390625

Calculate the square root of the right side: 4.2884292

Break this problem into two subproblems by setting 
(y + 1.125) equal to 4.2884292 and -4.2884292.


Subproblem 1
y + 1.125 = 4.2884292

Simplifying
y + 1.125 = 4.2884292

Reorder the terms:
1.125 + y = 4.2884292

Solving
1.125 + y = 4.2884292

Solving for variable 'y'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + y = 4.2884292 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + y = 4.2884292 + -1.125
y = 4.2884292 + -1.125

Combine like terms: 4.2884292 + -1.125 = 3.1634292
y = 3.1634292

Simplifying
y = 3.1634292


Subproblem 2
y + 1.125 = -4.2884292

Simplifying
y + 1.125 = -4.2884292

Reorder the terms:
1.125 + y = -4.2884292

Solving
1.125 + y = -4.2884292

Solving for variable 'y'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + y = -4.2884292 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + y = -4.2884292 + -1.125
y = -4.2884292 + -1.125

Combine like terms: -4.2884292 + -1.125 = -5.4134292
y = -5.4134292

Simplifying
y = -5.4134292


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.1634292, -5.4134292}

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