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

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

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

Reorder the terms:
-8n(-5 + n) = -2(4n + 11)
(-5 * -8n + n * -8n) = -2(4n + 11)
(40n + -8n2) = -2(4n + 11)

Reorder the terms:
40n + -8n2 = -2(11 + 4n)
40n + -8n2 = (11 * -2 + 4n * -2)
40n + -8n2 = (-22 + -8n)

Solving
40n + -8n2 = -22 + -8n

Solving for variable 'n'.

Reorder the terms:
22 + 40n + 8n + -8n2 = -22 + -8n + 22 + 8n

Combine like terms: 40n + 8n = 48n
22 + 48n + -8n2 = -22 + -8n + 22 + 8n

Reorder the terms:
22 + 48n + -8n2 = -22 + 22 + -8n + 8n

Combine like terms: -22 + 22 = 0
22 + 48n + -8n2 = 0 + -8n + 8n
22 + 48n + -8n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
22 + 48n + -8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + 24n + -4n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + 24n + -4n2)' equal to zero and attempt to solve:

Simplifying
11 + 24n + -4n2 = 0

Solving
11 + 24n + -4n2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.75 + -6n + n2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -6n + 2.75 + n2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -6n + n2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -6n + n2 = 0 + 2.75
-6n + n2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-6n + n2 = 2.75

The n term is -6n.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6n + 9 + n2 = 2.75 + 9

Reorder the terms:
9 + -6n + n2 = 2.75 + 9

Combine like terms: 2.75 + 9 = 11.75
9 + -6n + n2 = 11.75

Factor a perfect square on the left side:
(n + -3)(n + -3) = 11.75

Calculate the square root of the right side: 3.4278273

Break this problem into two subproblems by setting 
(n + -3) equal to 3.4278273 and -3.4278273.

Subproblem 1
n + -3 = 3.4278273

Simplifying
n + -3 = 3.4278273

Reorder the terms:
-3 + n = 3.4278273

Solving
-3 + n = 3.4278273

Solving for variable 'n'.

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

Add '3' to each side of the equation.
-3 + 3 + n = 3.4278273 + 3

Combine like terms: -3 + 3 = 0
0 + n = 3.4278273 + 3
n = 3.4278273 + 3

Combine like terms: 3.4278273 + 3 = 6.4278273
n = 6.4278273

Simplifying
n = 6.4278273

Subproblem 2
n + -3 = -3.4278273

Simplifying
n + -3 = -3.4278273

Reorder the terms:
-3 + n = -3.4278273

Solving
-3 + n = -3.4278273

Solving for variable 'n'.

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

Add '3' to each side of the equation.
-3 + 3 + n = -3.4278273 + 3

Combine like terms: -3 + 3 = 0
0 + n = -3.4278273 + 3
n = -3.4278273 + 3

Combine like terms: -3.4278273 + 3 = -0.4278273
n = -0.4278273

Simplifying
n = -0.4278273

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.4278273, -0.4278273}
Solution
n = {6.4278273, -0.4278273}