(y-8)(y+8)=64y

Solution for (y-8)(y+8)=64y equation:

Simplifying
(y + -8)(y + 8) = 64y

Reorder the terms:
(-8 + y)(y + 8) = 64y

Reorder the terms:
(-8 + y)(8 + y) = 64y

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

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

Solving
-64 + y2 = 64y

Solving for variable 'y'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is -64y.  Take half its coefficient (-32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
-64y + 1024 + y2 = 64 + 1024

Reorder the terms:
1024 + -64y + y2 = 64 + 1024

Combine like terms: 64 + 1024 = 1088
1024 + -64y + y2 = 1088

Factor a perfect square on the left side:
(y + -32)(y + -32) = 1088

Calculate the square root of the right side: 32.984845005

Break this problem into two subproblems by setting 
(y + -32) equal to 32.984845005 and -32.984845005.

Subproblem 1
y + -32 = 32.984845005

Simplifying
y + -32 = 32.984845005

Reorder the terms:
-32 + y = 32.984845005

Solving
-32 + y = 32.984845005

Solving for variable 'y'.

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

Add '32' to each side of the equation.
-32 + 32 + y = 32.984845005 + 32

Combine like terms: -32 + 32 = 0
0 + y = 32.984845005 + 32
y = 32.984845005 + 32

Combine like terms: 32.984845005 + 32 = 64.984845005
y = 64.984845005

Simplifying
y = 64.984845005

Subproblem 2
y + -32 = -32.984845005

Simplifying
y + -32 = -32.984845005

Reorder the terms:
-32 + y = -32.984845005

Solving
-32 + y = -32.984845005

Solving for variable 'y'.

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

Add '32' to each side of the equation.
-32 + 32 + y = -32.984845005 + 32

Combine like terms: -32 + 32 = 0
0 + y = -32.984845005 + 32
y = -32.984845005 + 32

Combine like terms: -32.984845005 + 32 = -0.984845005
y = -0.984845005

Simplifying
y = -0.984845005

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {64.984845005, -0.984845005}