(y+5)(y-3)=5

Solution for (y+5)(y-3)=5 equation:

Simplifying
(y + 5)(y + -3) = 5

Reorder the terms:
(5 + y)(y + -3) = 5

Reorder the terms:
(5 + y)(-3 + y) = 5

Multiply (5 + y) * (-3 + y)
(5(-3 + y) + y(-3 + y)) = 5
((-3 * 5 + y * 5) + y(-3 + y)) = 5
((-15 + 5y) + y(-3 + y)) = 5
(-15 + 5y + (-3 * y + y * y)) = 5
(-15 + 5y + (-3y + y2)) = 5

Combine like terms: 5y + -3y = 2y
(-15 + 2y + y2) = 5

Solving
-15 + 2y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
-15 + -5 + 2y + y2 = 5 + -5

Combine like terms: -15 + -5 = -20
-20 + 2y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-20 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 2y + 20 + y2 = 0 + 20

Reorder the terms:
-20 + 20 + 2y + y2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 2y + y2 = 0 + 20
2y + y2 = 0 + 20

Combine like terms: 0 + 20 = 20
2y + y2 = 20

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 20 + 1

Reorder the terms:
1 + 2y + y2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + 2y + y2 = 21

Factor a perfect square on the left side:
(y + 1)(y + 1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(y + 1) equal to 4.582575695 and -4.582575695.

Subproblem 1
y + 1 = 4.582575695

Simplifying
y + 1 = 4.582575695

Reorder the terms:
1 + y = 4.582575695

Solving
1 + y = 4.582575695

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 4.582575695 + -1

Combine like terms: 1 + -1 = 0
0 + y = 4.582575695 + -1
y = 4.582575695 + -1

Combine like terms: 4.582575695 + -1 = 3.582575695
y = 3.582575695

Simplifying
y = 3.582575695

Subproblem 2
y + 1 = -4.582575695

Simplifying
y + 1 = -4.582575695

Reorder the terms:
1 + y = -4.582575695

Solving
1 + y = -4.582575695

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -4.582575695 + -1

Combine like terms: 1 + -1 = 0
0 + y = -4.582575695 + -1
y = -4.582575695 + -1

Combine like terms: -4.582575695 + -1 = -5.582575695
y = -5.582575695

Simplifying
y = -5.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.582575695, -5.582575695}