(5n^3-n^5-3n^4)+(-14n^3+12n^5+13n^4)=

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Solution for (5n^3-n^5-3n^4)+(-14n^3+12n^5+13n^4)= equation: 


Simplifying
(5n3 + -1n5 + -3n4) + (-14n3 + 12n5 + 13n4) = 0

Reorder the terms:
(5n3 + -3n4 + -1n5) + (-14n3 + 12n5 + 13n4) = 0

Remove parenthesis around (5n3 + -3n4 + -1n5)
5n3 + -3n4 + -1n5 + (-14n3 + 12n5 + 13n4) = 0

Reorder the terms:
5n3 + -3n4 + -1n5 + (-14n3 + 13n4 + 12n5) = 0

Remove parenthesis around (-14n3 + 13n4 + 12n5)
5n3 + -3n4 + -1n5 + -14n3 + 13n4 + 12n5 = 0

Reorder the terms:
5n3 + -14n3 + -3n4 + 13n4 + -1n5 + 12n5 = 0

Combine like terms: 5n3 + -14n3 = -9n3
-9n3 + -3n4 + 13n4 + -1n5 + 12n5 = 0

Combine like terms: -3n4 + 13n4 = 10n4
-9n3 + 10n4 + -1n5 + 12n5 = 0

Combine like terms: -1n5 + 12n5 = 11n5
-9n3 + 10n4 + 11n5 = 0

Solving
-9n3 + 10n4 + 11n5 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n3'.
n3(-9 + 10n + 11n2) = 0


Subproblem 1
Set the factor 'n3' equal to zero and attempt to solve:

Simplifying
n3 = 0

Solving
n3 = 0

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

Simplifying
n3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-9 + 10n + 11n2)' equal to zero and attempt to solve:

Simplifying
-9 + 10n + 11n2 = 0

Solving
-9 + 10n + 11n2 = 0

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

Divide each side by '11'.
-0.8181818182 + 0.9090909091n + n2 = 0

Move the constant term to the right:

Add '0.8181818182' to each side of the equation.
-0.8181818182 + 0.9090909091n + 0.8181818182 + n2 = 0 + 0.8181818182

Reorder the terms:
-0.8181818182 + 0.8181818182 + 0.9090909091n + n2 = 0 + 0.8181818182

Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000
0.0000000000 + 0.9090909091n + n2 = 0 + 0.8181818182
0.9090909091n + n2 = 0 + 0.8181818182

Combine like terms: 0 + 0.8181818182 = 0.8181818182
0.9090909091n + n2 = 0.8181818182

The n term is 0.9090909091n.  Take half its coefficient (0.4545454546).
Square it (0.2066115703) and add it to both sides.

Add '0.2066115703' to each side of the equation.
0.9090909091n + 0.2066115703 + n2 = 0.8181818182 + 0.2066115703

Reorder the terms:
0.2066115703 + 0.9090909091n + n2 = 0.8181818182 + 0.2066115703

Combine like terms: 0.8181818182 + 0.2066115703 = 1.0247933885
0.2066115703 + 0.9090909091n + n2 = 1.0247933885

Factor a perfect square on the left side:
(n + 0.4545454546)(n + 0.4545454546) = 1.0247933885

Calculate the square root of the right side: 1.012320793

Break this problem into two subproblems by setting 
(n + 0.4545454546) equal to 1.012320793 and -1.012320793.


Subproblem 1
n + 0.4545454546 = 1.012320793

Simplifying
n + 0.4545454546 = 1.012320793

Reorder the terms:
0.4545454546 + n = 1.012320793

Solving
0.4545454546 + n = 1.012320793

Solving for variable 'n'.

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

Add '-0.4545454546' to each side of the equation.
0.4545454546 + -0.4545454546 + n = 1.012320793 + -0.4545454546

Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000
0.0000000000 + n = 1.012320793 + -0.4545454546
n = 1.012320793 + -0.4545454546

Combine like terms: 1.012320793 + -0.4545454546 = 0.5577753384
n = 0.5577753384

Simplifying
n = 0.5577753384


Subproblem 2
n + 0.4545454546 = -1.012320793

Simplifying
n + 0.4545454546 = -1.012320793

Reorder the terms:
0.4545454546 + n = -1.012320793

Solving
0.4545454546 + n = -1.012320793

Solving for variable 'n'.

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

Add '-0.4545454546' to each side of the equation.
0.4545454546 + -0.4545454546 + n = -1.012320793 + -0.4545454546

Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000
0.0000000000 + n = -1.012320793 + -0.4545454546
n = -1.012320793 + -0.4545454546

Combine like terms: -1.012320793 + -0.4545454546 = -1.4668662476
n = -1.4668662476

Simplifying
n = -1.4668662476


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.5577753384, -1.4668662476}
Solution
n = {0.5577753384, -1.4668662476}

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