(6n^2-5n^3)+(n^3+5n^2)=0

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Solution for (6n^2-5n^3)+(n^3+5n^2)=0 equation: 


Simplifying
(6n2 + -5n3) + (n3 + 5n2) = 0

Remove parenthesis around (6n2 + -5n3)
6n2 + -5n3 + (n3 + 5n2) = 0

Reorder the terms:
6n2 + -5n3 + (5n2 + n3) = 0

Remove parenthesis around (5n2 + n3)
6n2 + -5n3 + 5n2 + n3 = 0

Reorder the terms:
6n2 + 5n2 + -5n3 + n3 = 0

Combine like terms: 6n2 + 5n2 = 11n2
11n2 + -5n3 + n3 = 0

Combine like terms: -5n3 + n3 = -4n3
11n2 + -4n3 = 0

Solving
11n2 + -4n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(11 + -4n) = 0


Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}

Subproblem 2
Set the factor '(11 + -4n)' equal to zero and attempt to solve:

Simplifying
11 + -4n = 0

Solving
11 + -4n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4n = 0 + -11
-4n = 0 + -11

Combine like terms: 0 + -11 = -11
-4n = -11

Divide each side by '-4'.
n = 2.75

Simplifying
n = 2.75
Solution
n = {0, 2.75}

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