(y+8)(y-9)=52

Solution for (y+8)(y-9)=52 equation:

Simplifying
(y + 8)(y + -9) = 52

Reorder the terms:
(8 + y)(y + -9) = 52

Reorder the terms:
(8 + y)(-9 + y) = 52

Multiply (8 + y) * (-9 + y)
(8(-9 + y) + y(-9 + y)) = 52
((-9 * 8 + y * 8) + y(-9 + y)) = 52
((-72 + 8y) + y(-9 + y)) = 52
(-72 + 8y + (-9 * y + y * y)) = 52
(-72 + 8y + (-9y + y2)) = 52

Combine like terms: 8y + -9y = -1y
(-72 + -1y + y2) = 52

Solving
-72 + -1y + y2 = 52

Solving for variable 'y'.

Reorder the terms:
-72 + -52 + -1y + y2 = 52 + -52

Combine like terms: -72 + -52 = -124
-124 + -1y + y2 = 52 + -52

Combine like terms: 52 + -52 = 0
-124 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '124' to each side of the equation.
-124 + -1y + 124 + y2 = 0 + 124

Reorder the terms:
-124 + 124 + -1y + y2 = 0 + 124

Combine like terms: -124 + 124 = 0
0 + -1y + y2 = 0 + 124
-1y + y2 = 0 + 124

Combine like terms: 0 + 124 = 124
-1y + y2 = 124

The y term is -1y.  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 = 124 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 124 + 0.25

Combine like terms: 124 + 0.25 = 124.25
0.25 + -1y + y2 = 124.25

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 124.25

Calculate the square root of the right side: 11.146748405

Break this problem into two subproblems by setting 
(y + -0.5) equal to 11.146748405 and -11.146748405.

Subproblem 1
y + -0.5 = 11.146748405

Simplifying
y + -0.5 = 11.146748405

Reorder the terms:
-0.5 + y = 11.146748405

Solving
-0.5 + y = 11.146748405

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 = 11.146748405 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 11.146748405 + 0.5
y = 11.146748405 + 0.5

Combine like terms: 11.146748405 + 0.5 = 11.646748405
y = 11.646748405

Simplifying
y = 11.646748405

Subproblem 2
y + -0.5 = -11.146748405

Simplifying
y + -0.5 = -11.146748405

Reorder the terms:
-0.5 + y = -11.146748405

Solving
-0.5 + y = -11.146748405

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 = -11.146748405 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -11.146748405 + 0.5
y = -11.146748405 + 0.5

Combine like terms: -11.146748405 + 0.5 = -10.646748405
y = -10.646748405

Simplifying
y = -10.646748405

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.646748405, -10.646748405}