112-504n=567n^2

Solution for 112-504n=567n^2 equation:

Simplifying
112 + -504n = 567n2

Solving
112 + -504n = 567n2

Solving for variable 'n'.

Combine like terms: 567n2 + -567n2 = 0
112 + -504n + -567n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(16 + -72n + -81n2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(16 + -72n + -81n2)' equal to zero and attempt to solve:

Simplifying
16 + -72n + -81n2 = 0

Solving
16 + -72n + -81n2 = 0

Begin completing the square.  Divide all terms by
-81 the coefficient of the squared term: 

Divide each side by '-81'.
-0.1975308642 + 0.8888888889n + n2 = 0

Move the constant term to the right:

Add '0.1975308642' to each side of the equation.
-0.1975308642 + 0.8888888889n + 0.1975308642 + n2 = 0 + 0.1975308642

Reorder the terms:
-0.1975308642 + 0.1975308642 + 0.8888888889n + n2 = 0 + 0.1975308642

Combine like terms: -0.1975308642 + 0.1975308642 = 0.0000000000
0.0000000000 + 0.8888888889n + n2 = 0 + 0.1975308642
0.8888888889n + n2 = 0 + 0.1975308642

Combine like terms: 0 + 0.1975308642 = 0.1975308642
0.8888888889n + n2 = 0.1975308642

The n term is 0.8888888889n.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889n + 0.1975308642 + n2 = 0.1975308642 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889n + n2 = 0.1975308642 + 0.1975308642

Combine like terms: 0.1975308642 + 0.1975308642 = 0.3950617284
0.1975308642 + 0.8888888889n + n2 = 0.3950617284

Factor a perfect square on the left side:
(n + 0.4444444445)(n + 0.4444444445) = 0.3950617284

Calculate the square root of the right side: 0.628539361

Break this problem into two subproblems by setting 
(n + 0.4444444445) equal to 0.628539361 and -0.628539361.

Subproblem 1
n + 0.4444444445 = 0.628539361

Simplifying
n + 0.4444444445 = 0.628539361

Reorder the terms:
0.4444444445 + n = 0.628539361

Solving
0.4444444445 + n = 0.628539361

Solving for variable 'n'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + n = 0.628539361 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + n = 0.628539361 + -0.4444444445
n = 0.628539361 + -0.4444444445

Combine like terms: 0.628539361 + -0.4444444445 = 0.1840949165
n = 0.1840949165

Simplifying
n = 0.1840949165

Subproblem 2
n + 0.4444444445 = -0.628539361

Simplifying
n + 0.4444444445 = -0.628539361

Reorder the terms:
0.4444444445 + n = -0.628539361

Solving
0.4444444445 + n = -0.628539361

Solving for variable 'n'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + n = -0.628539361 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + n = -0.628539361 + -0.4444444445
n = -0.628539361 + -0.4444444445

Combine like terms: -0.628539361 + -0.4444444445 = -1.0729838055
n = -1.0729838055

Simplifying
n = -1.0729838055

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.1840949165, -1.0729838055}
Solution
n = {0.1840949165, -1.0729838055}