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

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


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

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

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

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

Combine like terms: -8y + 8y = 0
y = (-64 + 0 + y2)
y = (-64 + y2)

Solving
y = -64 + y2

Solving for variable 'y'.

Reorder the terms:
64 + y + -1y2 = -64 + y2 + 64 + -1y2

Reorder the terms:
64 + y + -1y2 = -64 + 64 + y2 + -1y2

Combine like terms: -64 + 64 = 0
64 + y + -1y2 = 0 + y2 + -1y2
64 + y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
64 + y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-64 + -1y + y2 = 0

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -1y + 64 + y2 = 0 + 64

Reorder the terms:
-64 + 64 + -1y + y2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -1y + y2 = 0 + 64
-1y + y2 = 0 + 64

Combine like terms: 0 + 64 = 64
-1y + y2 = 64

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 64 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 64 + 0.25

Combine like terms: 64 + 0.25 = 64.25
0.25 + -1y + y2 = 64.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(y + 0.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
y + 0.5 = 8.015609771

Simplifying
y + 0.5 = 8.015609771

Reorder the terms:
0.5 + y = 8.015609771

Solving
0.5 + y = 8.015609771

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 8.015609771 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 8.015609771 + -0.5
y = 8.015609771 + -0.5

Combine like terms: 8.015609771 + -0.5 = 7.515609771
y = 7.515609771

Simplifying
y = 7.515609771


Subproblem 2
y + 0.5 = -8.015609771

Simplifying
y + 0.5 = -8.015609771

Reorder the terms:
0.5 + y = -8.015609771

Solving
0.5 + y = -8.015609771

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -8.015609771 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -8.015609771 + -0.5
y = -8.015609771 + -0.5

Combine like terms: -8.015609771 + -0.5 = -8.515609771
y = -8.515609771

Simplifying
y = -8.515609771


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.515609771, -8.515609771}

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