6n^2=-12n-1

Solution for 6n^2=-12n-1 equation:

Simplifying
6n2 = -12n + -1

Reorder the terms:
6n2 = -1 + -12n

Solving
6n2 = -1 + -12n

Solving for variable 'n'.

Reorder the terms:
1 + 12n + 6n2 = -1 + -12n + 1 + 12n

Reorder the terms:
1 + 12n + 6n2 = -1 + 1 + -12n + 12n

Combine like terms: -1 + 1 = 0
1 + 12n + 6n2 = 0 + -12n + 12n
1 + 12n + 6n2 = -12n + 12n

Combine like terms: -12n + 12n = 0
1 + 12n + 6n2 = 0

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

Divide each side by '6'.
0.1666666667 + 2n + n2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 2n + -0.1666666667 + n2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 2n + n2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 2n + n2 = 0 + -0.1666666667
2n + n2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
2n + n2 = -0.1666666667

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = -0.1666666667 + 1

Reorder the terms:
1 + 2n + n2 = -0.1666666667 + 1

Combine like terms: -0.1666666667 + 1 = 0.8333333333
1 + 2n + n2 = 0.8333333333

Factor a perfect square on the left side:
(n + 1)(n + 1) = 0.8333333333

Calculate the square root of the right side: 0.912870929

Break this problem into two subproblems by setting 
(n + 1) equal to 0.912870929 and -0.912870929.

Subproblem 1
n + 1 = 0.912870929

Simplifying
n + 1 = 0.912870929

Reorder the terms:
1 + n = 0.912870929

Solving
1 + n = 0.912870929

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 0.912870929 + -1

Combine like terms: 1 + -1 = 0
0 + n = 0.912870929 + -1
n = 0.912870929 + -1

Combine like terms: 0.912870929 + -1 = -0.087129071
n = -0.087129071

Simplifying
n = -0.087129071

Subproblem 2
n + 1 = -0.912870929

Simplifying
n + 1 = -0.912870929

Reorder the terms:
1 + n = -0.912870929

Solving
1 + n = -0.912870929

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -0.912870929 + -1

Combine like terms: 1 + -1 = 0
0 + n = -0.912870929 + -1
n = -0.912870929 + -1

Combine like terms: -0.912870929 + -1 = -1.912870929
n = -1.912870929

Simplifying
n = -1.912870929

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.087129071, -1.912870929}