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

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


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

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

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

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

Reorder the terms:
-32 + 4y + y2 = 7 + -1[15 + -1y(2 + y)]
-32 + 4y + y2 = 7 + -1[15 + (2 * -1y + y * -1y)]
-32 + 4y + y2 = 7 + -1[15 + (-2y + -1y2)]
-32 + 4y + y2 = 7 + [15 * -1 + -2y * -1 + -1y2 * -1]
-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 + -1y2 = -8 + 2y + 1y2 + 8 + -2y + -1y2

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

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

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

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

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

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

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

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + y)' equal to zero and attempt to solve:

Simplifying
-12 + y = 0

Solving
-12 + y = 0

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

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

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

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

Simplifying
y = 12
Solution
y = {12}

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