(y-5)(y+5)=4+y

Solution for (y-5)(y+5)=4+y equation:

Simplifying
(y + -5)(y + 5) = 4 + y

Reorder the terms:
(-5 + y)(y + 5) = 4 + y

Reorder the terms:
(-5 + y)(5 + y) = 4 + y

Multiply (-5 + y) * (5 + y)
(-5(5 + y) + y(5 + y)) = 4 + y
((5 * -5 + y * -5) + y(5 + y)) = 4 + y
((-25 + -5y) + y(5 + y)) = 4 + y
(-25 + -5y + (5 * y + y * y)) = 4 + y
(-25 + -5y + (5y + y2)) = 4 + y

Combine like terms: -5y + 5y = 0
(-25 + 0 + y2) = 4 + y
(-25 + y2) = 4 + y

Solving
-25 + y2 = 4 + y

Solving for variable 'y'.

Reorder the terms:
-25 + -4 + -1y + y2 = 4 + y + -4 + -1y

Combine like terms: -25 + -4 = -29
-29 + -1y + y2 = 4 + y + -4 + -1y

Reorder the terms:
-29 + -1y + y2 = 4 + -4 + y + -1y

Combine like terms: 4 + -4 = 0
-29 + -1y + y2 = 0 + y + -1y
-29 + -1y + y2 = y + -1y

Combine like terms: y + -1y = 0
-29 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -1y + 29 + y2 = 0 + 29

Reorder the terms:
-29 + 29 + -1y + y2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -1y + y2 = 0 + 29
-1y + y2 = 0 + 29

Combine like terms: 0 + 29 = 29
-1y + y2 = 29

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 = 29 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 29 + 0.25

Combine like terms: 29 + 0.25 = 29.25
0.25 + -1y + y2 = 29.25

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(y + -0.5) equal to 5.408326913 and -5.408326913.

Subproblem 1
y + -0.5 = 5.408326913

Simplifying
y + -0.5 = 5.408326913

Reorder the terms:
-0.5 + y = 5.408326913

Solving
-0.5 + y = 5.408326913

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 = 5.408326913 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 5.408326913 + 0.5
y = 5.408326913 + 0.5

Combine like terms: 5.408326913 + 0.5 = 5.908326913
y = 5.908326913

Simplifying
y = 5.908326913

Subproblem 2
y + -0.5 = -5.408326913

Simplifying
y + -0.5 = -5.408326913

Reorder the terms:
-0.5 + y = -5.408326913

Solving
-0.5 + y = -5.408326913

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 = -5.408326913 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -5.408326913 + 0.5
y = -5.408326913 + 0.5

Combine like terms: -5.408326913 + 0.5 = -4.908326913
y = -4.908326913

Simplifying
y = -4.908326913

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.908326913, -4.908326913}