9n^2+31n+12=0

Solution for 9n^2+31n+12=0 equation:

Simplifying
9n2 + 31n + 12 = 0

Reorder the terms:
12 + 31n + 9n2 = 0

Solving
12 + 31n + 9n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + n)(4 + 9n) = 0

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

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(4 + 9n)' equal to zero and attempt to solve:

Simplifying
4 + 9n = 0

Solving
4 + 9n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 9n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9n = 0 + -4
9n = 0 + -4

Combine like terms: 0 + -4 = -4
9n = -4

Divide each side by '9'.
n = -0.4444444444

Simplifying
n = -0.4444444444
Solution
n = {-3, -0.4444444444}