(y+1)(y-1)=y+4y+4

Solution for (y+1)(y-1)=y+4y+4 equation:

Simplifying
(y + 1)(y + -1) = y + 4y + 4

Reorder the terms:
(1 + y)(y + -1) = y + 4y + 4

Reorder the terms:
(1 + y)(-1 + y) = y + 4y + 4

Multiply (1 + y) * (-1 + y)
(1(-1 + y) + y(-1 + y)) = y + 4y + 4
((-1 * 1 + y * 1) + y(-1 + y)) = y + 4y + 4
((-1 + 1y) + y(-1 + y)) = y + 4y + 4
(-1 + 1y + (-1 * y + y * y)) = y + 4y + 4
(-1 + 1y + (-1y + y2)) = y + 4y + 4

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

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

Combine like terms: y + 4y = 5y
-1 + y2 = 4 + 5y

Solving
-1 + y2 = 4 + 5y

Solving for variable 'y'.

Reorder the terms:
-1 + -4 + -5y + y2 = 4 + 5y + -4 + -5y

Combine like terms: -1 + -4 = -5
-5 + -5y + y2 = 4 + 5y + -4 + -5y

Reorder the terms:
-5 + -5y + y2 = 4 + -4 + 5y + -5y

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

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

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -5y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + -5y + y2 = 0 + 5

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

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

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = 5 + 6.25

Reorder the terms:
6.25 + -5y + y2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + -5y + y2 = 11.25

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(y + -2.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
y + -2.5 = 3.354101966

Simplifying
y + -2.5 = 3.354101966

Reorder the terms:
-2.5 + y = 3.354101966

Solving
-2.5 + y = 3.354101966

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = 3.354101966 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 3.354101966 + 2.5
y = 3.354101966 + 2.5

Combine like terms: 3.354101966 + 2.5 = 5.854101966
y = 5.854101966

Simplifying
y = 5.854101966

Subproblem 2
y + -2.5 = -3.354101966

Simplifying
y + -2.5 = -3.354101966

Reorder the terms:
-2.5 + y = -3.354101966

Solving
-2.5 + y = -3.354101966

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = -3.354101966 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -3.354101966 + 2.5
y = -3.354101966 + 2.5

Combine like terms: -3.354101966 + 2.5 = -0.854101966
y = -0.854101966

Simplifying
y = -0.854101966

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.854101966, -0.854101966}