(n^2+12)=1n(-9n-2)

Solution for (n^2+12)=1n(-9n-2) equation:

Simplifying
(n2 + 12) = 1n(-9n + -2)

Reorder the terms:
(12 + n2) = 1n(-9n + -2)

Remove parenthesis around (12 + n2)
12 + n2 = 1n(-9n + -2)

Reorder the terms:
12 + n2 = 1n(-2 + -9n)
12 + n2 = (-2 * 1n + -9n * 1n)
12 + n2 = (-2n + -9n2)

Solving
12 + n2 = -2n + -9n2

Solving for variable 'n'.

Reorder the terms:
12 + 2n + n2 + 9n2 = -2n + -9n2 + 2n + 9n2

Combine like terms: n2 + 9n2 = 10n2
12 + 2n + 10n2 = -2n + -9n2 + 2n + 9n2

Reorder the terms:
12 + 2n + 10n2 = -2n + 2n + -9n2 + 9n2

Combine like terms: -2n + 2n = 0
12 + 2n + 10n2 = 0 + -9n2 + 9n2
12 + 2n + 10n2 = -9n2 + 9n2

Combine like terms: -9n2 + 9n2 = 0
12 + 2n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + n + 5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + n + 5n2)' equal to zero and attempt to solve:

Simplifying
6 + n + 5n2 = 0

Solving
6 + n + 5n2 = 0

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

Divide each side by '5'.
1.2 + 0.2n + n2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 0.2n + -1.2 + n2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 0.2n + n2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 0.2n + n2 = 0 + -1.2
0.2n + n2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
0.2n + n2 = -1.2

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

Add '0.25' to each side of the equation.
0.2n + 0.25 + n2 = -1.2 + 0.25

Reorder the terms:
0.25 + 0.2n + n2 = -1.2 + 0.25

Combine like terms: -1.2 + 0.25 = -0.95
0.25 + 0.2n + n2 = -0.95

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.95

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.