9((9-2n+n^2))=79

Solution for 9((9-2n+n^2))=79 equation:

Simplifying
9(9 + -2n + n2) = 79
(9 * 9 + -2n * 9 + n2 * 9) = 79
(81 + -18n + 9n2) = 79

Solving
81 + -18n + 9n2 = 79

Solving for variable 'n'.

Reorder the terms:
81 + -79 + -18n + 9n2 = 79 + -79

Combine like terms: 81 + -79 = 2
2 + -18n + 9n2 = 79 + -79

Combine like terms: 79 + -79 = 0
2 + -18n + 9n2 = 0

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

Divide each side by '9'.
0.2222222222 + -2n + n2 = 0

Move the constant term to the right:

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -2n + -0.2222222222 + n2 = 0 + -0.2222222222

Reorder the terms:
0.2222222222 + -0.2222222222 + -2n + n2 = 0 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + -2n + n2 = 0 + -0.2222222222
-2n + n2 = 0 + -0.2222222222

Combine like terms: 0 + -0.2222222222 = -0.2222222222
-2n + n2 = -0.2222222222

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 = -0.2222222222 + 1

Reorder the terms:
1 + -2n + n2 = -0.2222222222 + 1

Combine like terms: -0.2222222222 + 1 = 0.7777777778
1 + -2n + n2 = 0.7777777778

Factor a perfect square on the left side:
(n + -1)(n + -1) = 0.7777777778

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(n + -1) equal to 0.881917104 and -0.881917104.

Subproblem 1
n + -1 = 0.881917104

Simplifying
n + -1 = 0.881917104

Reorder the terms:
-1 + n = 0.881917104

Solving
-1 + n = 0.881917104

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 = 0.881917104 + 1

Combine like terms: -1 + 1 = 0
0 + n = 0.881917104 + 1
n = 0.881917104 + 1

Combine like terms: 0.881917104 + 1 = 1.881917104
n = 1.881917104

Simplifying
n = 1.881917104

Subproblem 2
n + -1 = -0.881917104

Simplifying
n + -1 = -0.881917104

Reorder the terms:
-1 + n = -0.881917104

Solving
-1 + n = -0.881917104

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 = -0.881917104 + 1

Combine like terms: -1 + 1 = 0
0 + n = -0.881917104 + 1
n = -0.881917104 + 1

Combine like terms: -0.881917104 + 1 = 0.118082896
n = 0.118082896

Simplifying
n = 0.118082896

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.881917104, 0.118082896}