n*2.3(10-n)2.2=32.9

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Solution for n*2.3(10-n)2.2=32.9 equation: 


Simplifying
n * 2.3(10 + -1n) * 2.2 = 32.9

Reorder the terms for easier multiplication:
2.3 * 2.2n(10 + -1n) = 32.9

Multiply 2.3 * 2.2
5.06n(10 + -1n) = 32.9
(10 * 5.06n + -1n * 5.06n) = 32.9
(50.6n + -5.06n2) = 32.9

Solving
50.6n + -5.06n2 = 32.9

Solving for variable 'n'.

Reorder the terms:
-32.9 + 50.6n + -5.06n2 = 32.9 + -32.9

Combine like terms: 32.9 + -32.9 = 0.0
-32.9 + 50.6n + -5.06n2 = 0.0

Begin completing the square.  Divide all terms by
-5.06 the coefficient of the squared term: 

Divide each side by '-5.06'.
6.501976285 + -10n + n2 = 0

Move the constant term to the right:

Add '-6.501976285' to each side of the equation.
6.501976285 + -10n + -6.501976285 + n2 = 0 + -6.501976285

Reorder the terms:
6.501976285 + -6.501976285 + -10n + n2 = 0 + -6.501976285

Combine like terms: 6.501976285 + -6.501976285 = 0.000000000
0.000000000 + -10n + n2 = 0 + -6.501976285
-10n + n2 = 0 + -6.501976285

Combine like terms: 0 + -6.501976285 = -6.501976285
-10n + n2 = -6.501976285

The n term is -10n.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10n + 25 + n2 = -6.501976285 + 25

Reorder the terms:
25 + -10n + n2 = -6.501976285 + 25

Combine like terms: -6.501976285 + 25 = 18.498023715
25 + -10n + n2 = 18.498023715

Factor a perfect square on the left side:
(n + -5)(n + -5) = 18.498023715

Calculate the square root of the right side: 4.300932889

Break this problem into two subproblems by setting 
(n + -5) equal to 4.300932889 and -4.300932889.


Subproblem 1
n + -5 = 4.300932889

Simplifying
n + -5 = 4.300932889

Reorder the terms:
-5 + n = 4.300932889

Solving
-5 + n = 4.300932889

Solving for variable 'n'.

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

Add '5' to each side of the equation.
-5 + 5 + n = 4.300932889 + 5

Combine like terms: -5 + 5 = 0
0 + n = 4.300932889 + 5
n = 4.300932889 + 5

Combine like terms: 4.300932889 + 5 = 9.300932889
n = 9.300932889

Simplifying
n = 9.300932889


Subproblem 2
n + -5 = -4.300932889

Simplifying
n + -5 = -4.300932889

Reorder the terms:
-5 + n = -4.300932889

Solving
-5 + n = -4.300932889

Solving for variable 'n'.

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

Add '5' to each side of the equation.
-5 + 5 + n = -4.300932889 + 5

Combine like terms: -5 + 5 = 0
0 + n = -4.300932889 + 5
n = -4.300932889 + 5

Combine like terms: -4.300932889 + 5 = 0.699067111
n = 0.699067111

Simplifying
n = 0.699067111


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.300932889, 0.699067111}

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