2n^3-n^2-5n=0

Solution for 2n^3-n^2-5n=0 equation:

Simplifying
2n3 + -1n2 + -5n = 0

Reorder the terms:
-5n + -1n2 + 2n3 = 0

Solving
-5n + -1n2 + 2n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5 + -1n + 2n2) = 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 '(-5 + -1n + 2n2)' equal to zero and attempt to solve:

Simplifying
-5 + -1n + 2n2 = 0

Solving
-5 + -1n + 2n2 = 0

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

Divide each side by '2'.
-2.5 + -0.5n + n2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.5n + 2.5 + n2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.5n + n2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.5n + n2 = 0 + 2.5
-0.5n + n2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.5n + n2 = 2.5

The n term is -0.5n.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5n + 0.0625 + n2 = 2.5 + 0.0625

Reorder the terms:
0.0625 + -0.5n + n2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + -0.5n + n2 = 2.5625

Factor a perfect square on the left side:
(n + -0.25)(n + -0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(n + -0.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
n + -0.25 = 1.600781059

Simplifying
n + -0.25 = 1.600781059

Reorder the terms:
-0.25 + n = 1.600781059

Solving
-0.25 + n = 1.600781059

Solving for variable 'n'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + n = 1.600781059 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = 1.600781059 + 0.25
n = 1.600781059 + 0.25

Combine like terms: 1.600781059 + 0.25 = 1.850781059
n = 1.850781059

Simplifying
n = 1.850781059

Subproblem 2
n + -0.25 = -1.600781059

Simplifying
n + -0.25 = -1.600781059

Reorder the terms:
-0.25 + n = -1.600781059

Solving
-0.25 + n = -1.600781059

Solving for variable 'n'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + n = -1.600781059 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = -1.600781059 + 0.25
n = -1.600781059 + 0.25

Combine like terms: -1.600781059 + 0.25 = -1.350781059
n = -1.350781059

Simplifying
n = -1.350781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.850781059, -1.350781059}
Solution
n = {0, 1.850781059, -1.350781059}