5n(2-n)=-11

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

Simplifying
5n(2 + -1n) = -11
(2 * 5n + -1n * 5n) = -11
(10n + -5n2) = -11

Solving
10n + -5n2 = -11

Solving for variable 'n'.

Reorder the terms:
11 + 10n + -5n2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + 10n + -5n2 = 0

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

Divide each side by '-5'.
-2.2 + -2n + n2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -2n + 2.2 + n2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -2n + n2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -2n + n2 = 0 + 2.2
-2n + n2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-2n + n2 = 2.2

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 2.2 + 1

Reorder the terms:
1 + -2n + n2 = 2.2 + 1

Combine like terms: 2.2 + 1 = 3.2
1 + -2n + n2 = 3.2

Factor a perfect square on the left side:
(n + -1)(n + -1) = 3.2

Calculate the square root of the right side: 1.788854382

Break this problem into two subproblems by setting 
(n + -1) equal to 1.788854382 and -1.788854382.

Subproblem 1
n + -1 = 1.788854382

Simplifying
n + -1 = 1.788854382

Reorder the terms:
-1 + n = 1.788854382

Solving
-1 + n = 1.788854382

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = 1.788854382 + 1

Combine like terms: -1 + 1 = 0
0 + n = 1.788854382 + 1
n = 1.788854382 + 1

Combine like terms: 1.788854382 + 1 = 2.788854382
n = 2.788854382

Simplifying
n = 2.788854382

Subproblem 2
n + -1 = -1.788854382

Simplifying
n + -1 = -1.788854382

Reorder the terms:
-1 + n = -1.788854382

Solving
-1 + n = -1.788854382

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = -1.788854382 + 1

Combine like terms: -1 + 1 = 0
0 + n = -1.788854382 + 1
n = -1.788854382 + 1

Combine like terms: -1.788854382 + 1 = -0.788854382
n = -0.788854382

Simplifying
n = -0.788854382

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.788854382, -0.788854382}