y(y+4)+11=8(y+2)+(y-4)(4-5)

Solution for y(y+4)+11=8(y+2)+(y-4)(4-5) equation:

Simplifying
y(y + 4) + 11 = 8(y + 2) + (y + -4)(4 + -5)

Reorder the terms:
y(4 + y) + 11 = 8(y + 2) + (y + -4)(4 + -5)
(4 * y + y * y) + 11 = 8(y + 2) + (y + -4)(4 + -5)
(4y + y2) + 11 = 8(y + 2) + (y + -4)(4 + -5)

Reorder the terms:
11 + 4y + y2 = 8(y + 2) + (y + -4)(4 + -5)

Reorder the terms:
11 + 4y + y2 = 8(2 + y) + (y + -4)(4 + -5)
11 + 4y + y2 = (2 * 8 + y * 8) + (y + -4)(4 + -5)
11 + 4y + y2 = (16 + 8y) + (y + -4)(4 + -5)

Reorder the terms:
11 + 4y + y2 = 16 + 8y + (-4 + y)(4 + -5)

Combine like terms: 4 + -5 = -1
11 + 4y + y2 = 16 + 8y + (-4 + y)(-1)

Reorder the terms for easier multiplication:
11 + 4y + y2 = 16 + 8y + -1(-4 + y)
11 + 4y + y2 = 16 + 8y + (-4 * -1 + y * -1)
11 + 4y + y2 = 16 + 8y + (4 + -1y)

Reorder the terms:
11 + 4y + y2 = 16 + 4 + 8y + -1y

Combine like terms: 16 + 4 = 20
11 + 4y + y2 = 20 + 8y + -1y

Combine like terms: 8y + -1y = 7y
11 + 4y + y2 = 20 + 7y

Solving
11 + 4y + y2 = 20 + 7y

Solving for variable 'y'.

Reorder the terms:
11 + -20 + 4y + -7y + y2 = 20 + 7y + -20 + -7y

Combine like terms: 11 + -20 = -9
-9 + 4y + -7y + y2 = 20 + 7y + -20 + -7y

Combine like terms: 4y + -7y = -3y
-9 + -3y + y2 = 20 + 7y + -20 + -7y

Reorder the terms:
-9 + -3y + y2 = 20 + -20 + 7y + -7y

Combine like terms: 20 + -20 = 0
-9 + -3y + y2 = 0 + 7y + -7y
-9 + -3y + y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-9 + -3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -3y + 9 + y2 = 0 + 9

Reorder the terms:
-9 + 9 + -3y + y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -3y + y2 = 0 + 9
-3y + y2 = 0 + 9

Combine like terms: 0 + 9 = 9
-3y + y2 = 9

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 9 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 9 + 2.25

Combine like terms: 9 + 2.25 = 11.25
2.25 + -3y + y2 = 11.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(y + -1.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
y + -1.5 = 3.354101966

Simplifying
y + -1.5 = 3.354101966

Reorder the terms:
-1.5 + y = 3.354101966

Solving
-1.5 + y = 3.354101966

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 3.354101966 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 3.354101966 + 1.5
y = 3.354101966 + 1.5

Combine like terms: 3.354101966 + 1.5 = 4.854101966
y = 4.854101966

Simplifying
y = 4.854101966

Subproblem 2
y + -1.5 = -3.354101966

Simplifying
y + -1.5 = -3.354101966

Reorder the terms:
-1.5 + y = -3.354101966

Solving
-1.5 + y = -3.354101966

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -3.354101966 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -3.354101966 + 1.5
y = -3.354101966 + 1.5

Combine like terms: -3.354101966 + 1.5 = -1.854101966
y = -1.854101966

Simplifying
y = -1.854101966

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.854101966, -1.854101966}