5y(y+8)=-6(y-2)+94

Solution for 5y(y+8)=-6(y-2)+94 equation:

Simplifying
5y(y + 8) = -6(y + -2) + 94

Reorder the terms:
5y(8 + y) = -6(y + -2) + 94
(8 * 5y + y * 5y) = -6(y + -2) + 94
(40y + 5y2) = -6(y + -2) + 94

Reorder the terms:
40y + 5y2 = -6(-2 + y) + 94
40y + 5y2 = (-2 * -6 + y * -6) + 94
40y + 5y2 = (12 + -6y) + 94

Reorder the terms:
40y + 5y2 = 12 + 94 + -6y

Combine like terms: 12 + 94 = 106
40y + 5y2 = 106 + -6y

Solving
40y + 5y2 = 106 + -6y

Solving for variable 'y'.

Reorder the terms:
-106 + 40y + 6y + 5y2 = 106 + -6y + -106 + 6y

Combine like terms: 40y + 6y = 46y
-106 + 46y + 5y2 = 106 + -6y + -106 + 6y

Reorder the terms:
-106 + 46y + 5y2 = 106 + -106 + -6y + 6y

Combine like terms: 106 + -106 = 0
-106 + 46y + 5y2 = 0 + -6y + 6y
-106 + 46y + 5y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-106 + 46y + 5y2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-21.2 + 9.2y + y2 = 0

Move the constant term to the right:

Add '21.2' to each side of the equation.
-21.2 + 9.2y + 21.2 + y2 = 0 + 21.2

Reorder the terms:
-21.2 + 21.2 + 9.2y + y2 = 0 + 21.2

Combine like terms: -21.2 + 21.2 = 0.0
0.0 + 9.2y + y2 = 0 + 21.2
9.2y + y2 = 0 + 21.2

Combine like terms: 0 + 21.2 = 21.2
9.2y + y2 = 21.2

The y term is 9.2y.  Take half its coefficient (4.6).
Square it (21.16) and add it to both sides.

Add '21.16' to each side of the equation.
9.2y + 21.16 + y2 = 21.2 + 21.16

Reorder the terms:
21.16 + 9.2y + y2 = 21.2 + 21.16

Combine like terms: 21.2 + 21.16 = 42.36
21.16 + 9.2y + y2 = 42.36

Factor a perfect square on the left side:
(y + 4.6)(y + 4.6) = 42.36

Calculate the square root of the right side: 6.508456038

Break this problem into two subproblems by setting 
(y + 4.6) equal to 6.508456038 and -6.508456038.

Subproblem 1
y + 4.6 = 6.508456038

Simplifying
y + 4.6 = 6.508456038

Reorder the terms:
4.6 + y = 6.508456038

Solving
4.6 + y = 6.508456038

Solving for variable 'y'.

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

Add '-4.6' to each side of the equation.
4.6 + -4.6 + y = 6.508456038 + -4.6

Combine like terms: 4.6 + -4.6 = 0.0
0.0 + y = 6.508456038 + -4.6
y = 6.508456038 + -4.6

Combine like terms: 6.508456038 + -4.6 = 1.908456038
y = 1.908456038

Simplifying
y = 1.908456038

Subproblem 2
y + 4.6 = -6.508456038

Simplifying
y + 4.6 = -6.508456038

Reorder the terms:
4.6 + y = -6.508456038

Solving
4.6 + y = -6.508456038

Solving for variable 'y'.

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

Add '-4.6' to each side of the equation.
4.6 + -4.6 + y = -6.508456038 + -4.6

Combine like terms: 4.6 + -4.6 = 0.0
0.0 + y = -6.508456038 + -4.6
y = -6.508456038 + -4.6

Combine like terms: -6.508456038 + -4.6 = -11.108456038
y = -11.108456038

Simplifying
y = -11.108456038

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.908456038, -11.108456038}