9n^2+3n+7=-2

Solution for 9n^2+3n+7=-2 equation:

Simplifying
9n2 + 3n + 7 = -2

Reorder the terms:
7 + 3n + 9n2 = -2

Solving
7 + 3n + 9n2 = -2

Solving for variable 'n'.

Reorder the terms:
7 + 2 + 3n + 9n2 = -2 + 2

Combine like terms: 7 + 2 = 9
9 + 3n + 9n2 = -2 + 2

Combine like terms: -2 + 2 = 0
9 + 3n + 9n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + n + 3n2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + n + 3n2)' equal to zero and attempt to solve:

Simplifying
3 + n + 3n2 = 0

Solving
3 + n + 3n2 = 0

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

Divide each side by '3'.
1 + 0.3333333333n + n2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.3333333333n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + 0.3333333333n + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.3333333333n + n2 = 0 + -1
0.3333333333n + n2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.3333333333n + n2 = -1

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.
0.3333333333n + 0.25 + n2 = -1 + 0.25

Reorder the terms:
0.25 + 0.3333333333n + n2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + 0.3333333333n + n2 = -0.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.75

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.