2n-1+n^2+5n=0

Solution for 2n-1+n^2+5n=0 equation:

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

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

Combine like terms: 2n + 5n = 7n
-1 + 7n + n2 = 0

Solving
-1 + 7n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 7n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + 7n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 7n + n2 = 0 + 1
7n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
7n + n2 = 1

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = 1 + 12.25

Reorder the terms:
12.25 + 7n + n2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + 7n + n2 = 13.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(n + 3.5) equal to 3.640054945 and -3.640054945.

Subproblem 1
n + 3.5 = 3.640054945

Simplifying
n + 3.5 = 3.640054945

Reorder the terms:
3.5 + n = 3.640054945

Solving
3.5 + n = 3.640054945

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = 3.640054945 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = 3.640054945 + -3.5
n = 3.640054945 + -3.5

Combine like terms: 3.640054945 + -3.5 = 0.140054945
n = 0.140054945

Simplifying
n = 0.140054945

Subproblem 2
n + 3.5 = -3.640054945

Simplifying
n + 3.5 = -3.640054945

Reorder the terms:
3.5 + n = -3.640054945

Solving
3.5 + n = -3.640054945

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = -3.640054945 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = -3.640054945 + -3.5
n = -3.640054945 + -3.5

Combine like terms: -3.640054945 + -3.5 = -7.140054945
n = -7.140054945

Simplifying
n = -7.140054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.140054945, -7.140054945}