y=(y+8)(y+8)-2(y+8)-8

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


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

Reorder the terms:
y = (8 + y)(y + 8) + -2(y + 8) + -8

Reorder the terms:
y = (8 + y)(8 + y) + -2(y + 8) + -8

Multiply (8 + y) * (8 + y)
y = (8(8 + y) + y(8 + y)) + -2(y + 8) + -8
y = ((8 * 8 + y * 8) + y(8 + y)) + -2(y + 8) + -8
y = ((64 + 8y) + y(8 + y)) + -2(y + 8) + -8
y = (64 + 8y + (8 * y + y * y)) + -2(y + 8) + -8
y = (64 + 8y + (8y + y2)) + -2(y + 8) + -8

Combine like terms: 8y + 8y = 16y
y = (64 + 16y + y2) + -2(y + 8) + -8

Reorder the terms:
y = 64 + 16y + y2 + -2(8 + y) + -8
y = 64 + 16y + y2 + (8 * -2 + y * -2) + -8
y = 64 + 16y + y2 + (-16 + -2y) + -8

Reorder the terms:
y = 64 + -16 + -8 + 16y + -2y + y2

Combine like terms: 64 + -16 = 48
y = 48 + -8 + 16y + -2y + y2

Combine like terms: 48 + -8 = 40
y = 40 + 16y + -2y + y2

Combine like terms: 16y + -2y = 14y
y = 40 + 14y + y2

Solving
y = 40 + 14y + y2

Solving for variable 'y'.

Reorder the terms:
-40 + y + -14y + -1y2 = 40 + 14y + y2 + -40 + -14y + -1y2

Combine like terms: y + -14y = -13y
-40 + -13y + -1y2 = 40 + 14y + y2 + -40 + -14y + -1y2

Reorder the terms:
-40 + -13y + -1y2 = 40 + -40 + 14y + -14y + y2 + -1y2

Combine like terms: 40 + -40 = 0
-40 + -13y + -1y2 = 0 + 14y + -14y + y2 + -1y2
-40 + -13y + -1y2 = 14y + -14y + y2 + -1y2

Combine like terms: 14y + -14y = 0
-40 + -13y + -1y2 = 0 + y2 + -1y2
-40 + -13y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-40 + -13y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(40 + 13y + y2) = 0

Factor a trinomial.
-1((8 + y)(5 + y)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8

Subproblem 2
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Solution
y = {-8, -5}

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