100n+60n^2-n^3-525n=0

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Solution for 100n+60n^2-n^3-525n=0 equation: 


Simplifying
100n + 60n2 + -1n3 + -525n = 0

Reorder the terms:
100n + -525n + 60n2 + -1n3 = 0

Combine like terms: 100n + -525n = -425n
-425n + 60n2 + -1n3 = 0

Solving
-425n + 60n2 + -1n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-425 + 60n + -1n2) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-425 + 60n + -1n2)' equal to zero and attempt to solve:

Simplifying
-425 + 60n + -1n2 = 0

Solving
-425 + 60n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
425 + -60n + n2 = 0

Move the constant term to the right:

Add '-425' to each side of the equation.
425 + -60n + -425 + n2 = 0 + -425

Reorder the terms:
425 + -425 + -60n + n2 = 0 + -425

Combine like terms: 425 + -425 = 0
0 + -60n + n2 = 0 + -425
-60n + n2 = 0 + -425

Combine like terms: 0 + -425 = -425
-60n + n2 = -425

The n term is -60n.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60n + 900 + n2 = -425 + 900

Reorder the terms:
900 + -60n + n2 = -425 + 900

Combine like terms: -425 + 900 = 475
900 + -60n + n2 = 475

Factor a perfect square on the left side:
(n + -30)(n + -30) = 475

Calculate the square root of the right side: 21.794494718

Break this problem into two subproblems by setting 
(n + -30) equal to 21.794494718 and -21.794494718.


Subproblem 1
n + -30 = 21.794494718

Simplifying
n + -30 = 21.794494718

Reorder the terms:
-30 + n = 21.794494718

Solving
-30 + n = 21.794494718

Solving for variable 'n'.

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

Add '30' to each side of the equation.
-30 + 30 + n = 21.794494718 + 30

Combine like terms: -30 + 30 = 0
0 + n = 21.794494718 + 30
n = 21.794494718 + 30

Combine like terms: 21.794494718 + 30 = 51.794494718
n = 51.794494718

Simplifying
n = 51.794494718


Subproblem 2
n + -30 = -21.794494718

Simplifying
n + -30 = -21.794494718

Reorder the terms:
-30 + n = -21.794494718

Solving
-30 + n = -21.794494718

Solving for variable 'n'.

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

Add '30' to each side of the equation.
-30 + 30 + n = -21.794494718 + 30

Combine like terms: -30 + 30 = 0
0 + n = -21.794494718 + 30
n = -21.794494718 + 30

Combine like terms: -21.794494718 + 30 = 8.205505282
n = 8.205505282

Simplifying
n = 8.205505282


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {51.794494718, 8.205505282}
Solution
n = {0, 51.794494718, 8.205505282}

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