y^2-8y-32=0

Solution for y^2-8y-32=0 equation:

Simplifying
y2 + -8y + -32 = 0

Reorder the terms:
-32 + -8y + y2 = 0

Solving
-32 + -8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -8y + 32 + y2 = 0 + 32

Reorder the terms:
-32 + 32 + -8y + y2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -8y + y2 = 0 + 32
-8y + y2 = 0 + 32

Combine like terms: 0 + 32 = 32
-8y + y2 = 32

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = 32 + 16

Reorder the terms:
16 + -8y + y2 = 32 + 16

Combine like terms: 32 + 16 = 48
16 + -8y + y2 = 48

Factor a perfect square on the left side:
(y + -4)(y + -4) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(y + -4) equal to 6.92820323 and -6.92820323.

Subproblem 1
y + -4 = 6.92820323

Simplifying
y + -4 = 6.92820323

Reorder the terms:
-4 + y = 6.92820323

Solving
-4 + y = 6.92820323

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 6.92820323 + 4

Combine like terms: -4 + 4 = 0
0 + y = 6.92820323 + 4
y = 6.92820323 + 4

Combine like terms: 6.92820323 + 4 = 10.92820323
y = 10.92820323

Simplifying
y = 10.92820323

Subproblem 2
y + -4 = -6.92820323

Simplifying
y + -4 = -6.92820323

Reorder the terms:
-4 + y = -6.92820323

Solving
-4 + y = -6.92820323

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -6.92820323 + 4

Combine like terms: -4 + 4 = 0
0 + y = -6.92820323 + 4
y = -6.92820323 + 4

Combine like terms: -6.92820323 + 4 = -2.92820323
y = -2.92820323

Simplifying
y = -2.92820323

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.92820323, -2.92820323}