10n^2+12n=-1

Solution for 10n^2+12n=-1 equation:

Simplifying
10n2 + 12n = -1

Reorder the terms:
12n + 10n2 = -1

Solving
12n + 10n2 = -1

Solving for variable 'n'.

Reorder the terms:
1 + 12n + 10n2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 12n + 10n2 = 0

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

Divide each side by '10'.
0.1 + 1.2n + n2 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + 1.2n + -0.1 + n2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + 1.2n + n2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + 1.2n + n2 = 0 + -0.1
1.2n + n2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
1.2n + n2 = -0.1

The n term is 1.2n.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2n + 0.36 + n2 = -0.1 + 0.36

Reorder the terms:
0.36 + 1.2n + n2 = -0.1 + 0.36

Combine like terms: -0.1 + 0.36 = 0.26
0.36 + 1.2n + n2 = 0.26

Factor a perfect square on the left side:
(n + 0.6)(n + 0.6) = 0.26

Calculate the square root of the right side: 0.509901951

Break this problem into two subproblems by setting 
(n + 0.6) equal to 0.509901951 and -0.509901951.

Subproblem 1
n + 0.6 = 0.509901951

Simplifying
n + 0.6 = 0.509901951

Reorder the terms:
0.6 + n = 0.509901951

Solving
0.6 + n = 0.509901951

Solving for variable 'n'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + n = 0.509901951 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + n = 0.509901951 + -0.6
n = 0.509901951 + -0.6

Combine like terms: 0.509901951 + -0.6 = -0.090098049
n = -0.090098049

Simplifying
n = -0.090098049

Subproblem 2
n + 0.6 = -0.509901951

Simplifying
n + 0.6 = -0.509901951

Reorder the terms:
0.6 + n = -0.509901951

Solving
0.6 + n = -0.509901951

Solving for variable 'n'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + n = -0.509901951 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + n = -0.509901951 + -0.6
n = -0.509901951 + -0.6

Combine like terms: -0.509901951 + -0.6 = -1.109901951
n = -1.109901951

Simplifying
n = -1.109901951

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.090098049, -1.109901951}