3n^2-6n=-1

Solution for 3n^2-6n=-1 equation:

Simplifying
3n2 + -6n = -1

Reorder the terms:
-6n + 3n2 = -1

Solving
-6n + 3n2 = -1

Solving for variable 'n'.

Reorder the terms:
1 + -6n + 3n2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -6n + 3n2 = 0

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

Divide each side by '3'.
0.3333333333 + -2n + n2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2n + -0.3333333333 + n2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2n + n2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2n + n2 = 0 + -0.3333333333
-2n + n2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2n + n2 = -0.3333333333

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 = -0.3333333333 + 1

Reorder the terms:
1 + -2n + n2 = -0.3333333333 + 1

Combine like terms: -0.3333333333 + 1 = 0.6666666667
1 + -2n + n2 = 0.6666666667

Factor a perfect square on the left side:
(n + -1)(n + -1) = 0.6666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(n + -1) equal to 0.816496581 and -0.816496581.

Subproblem 1
n + -1 = 0.816496581

Simplifying
n + -1 = 0.816496581

Reorder the terms:
-1 + n = 0.816496581

Solving
-1 + n = 0.816496581

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 = 0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + n = 0.816496581 + 1
n = 0.816496581 + 1

Combine like terms: 0.816496581 + 1 = 1.816496581
n = 1.816496581

Simplifying
n = 1.816496581

Subproblem 2
n + -1 = -0.816496581

Simplifying
n + -1 = -0.816496581

Reorder the terms:
-1 + n = -0.816496581

Solving
-1 + n = -0.816496581

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 = -0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + n = -0.816496581 + 1
n = -0.816496581 + 1

Combine like terms: -0.816496581 + 1 = 0.183503419
n = 0.183503419

Simplifying
n = 0.183503419

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.816496581, 0.183503419}