n-2(n-2)9n+32=7

Solution for n-2(n-2)9n+32=7 equation:

Simplifying
n + -2(n + -2) * 9n + 32 = 7

Reorder the terms:
n + -2(-2 + n) * 9n + 32 = 7

Reorder the terms for easier multiplication:
n + -2 * 9n(-2 + n) + 32 = 7

Multiply -2 * 9
n + -18n(-2 + n) + 32 = 7
n + (-2 * -18n + n * -18n) + 32 = 7
n + (36n + -18n2) + 32 = 7

Reorder the terms:
32 + n + 36n + -18n2 = 7

Combine like terms: n + 36n = 37n
32 + 37n + -18n2 = 7

Solving
32 + 37n + -18n2 = 7

Solving for variable 'n'.

Reorder the terms:
32 + -7 + 37n + -18n2 = 7 + -7

Combine like terms: 32 + -7 = 25
25 + 37n + -18n2 = 7 + -7

Combine like terms: 7 + -7 = 0
25 + 37n + -18n2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-1.388888889 + -2.055555556n + n2 = 0

Move the constant term to the right:

Add '1.388888889' to each side of the equation.
-1.388888889 + -2.055555556n + 1.388888889 + n2 = 0 + 1.388888889

Reorder the terms:
-1.388888889 + 1.388888889 + -2.055555556n + n2 = 0 + 1.388888889

Combine like terms: -1.388888889 + 1.388888889 = 0.000000000
0.000000000 + -2.055555556n + n2 = 0 + 1.388888889
-2.055555556n + n2 = 0 + 1.388888889

Combine like terms: 0 + 1.388888889 = 1.388888889
-2.055555556n + n2 = 1.388888889

The n term is -2.055555556n.  Take half its coefficient (-1.027777778).
Square it (1.056327161) and add it to both sides.

Add '1.056327161' to each side of the equation.
-2.055555556n + 1.056327161 + n2 = 1.388888889 + 1.056327161

Reorder the terms:
1.056327161 + -2.055555556n + n2 = 1.388888889 + 1.056327161

Combine like terms: 1.388888889 + 1.056327161 = 2.44521605
1.056327161 + -2.055555556n + n2 = 2.44521605

Factor a perfect square on the left side:
(n + -1.027777778)(n + -1.027777778) = 2.44521605

Calculate the square root of the right side: 1.563718661

Break this problem into two subproblems by setting 
(n + -1.027777778) equal to 1.563718661 and -1.563718661.

Subproblem 1
n + -1.027777778 = 1.563718661

Simplifying
n + -1.027777778 = 1.563718661

Reorder the terms:
-1.027777778 + n = 1.563718661

Solving
-1.027777778 + n = 1.563718661

Solving for variable 'n'.

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

Add '1.027777778' to each side of the equation.
-1.027777778 + 1.027777778 + n = 1.563718661 + 1.027777778

Combine like terms: -1.027777778 + 1.027777778 = 0.000000000
0.000000000 + n = 1.563718661 + 1.027777778
n = 1.563718661 + 1.027777778

Combine like terms: 1.563718661 + 1.027777778 = 2.591496439
n = 2.591496439

Simplifying
n = 2.591496439

Subproblem 2
n + -1.027777778 = -1.563718661

Simplifying
n + -1.027777778 = -1.563718661

Reorder the terms:
-1.027777778 + n = -1.563718661

Solving
-1.027777778 + n = -1.563718661

Solving for variable 'n'.

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

Add '1.027777778' to each side of the equation.
-1.027777778 + 1.027777778 + n = -1.563718661 + 1.027777778

Combine like terms: -1.027777778 + 1.027777778 = 0.000000000
0.000000000 + n = -1.563718661 + 1.027777778
n = -1.563718661 + 1.027777778

Combine like terms: -1.563718661 + 1.027777778 = -0.535940883
n = -0.535940883

Simplifying
n = -0.535940883

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.591496439, -0.535940883}