12+31n=-7n^2

Solution for 12+31n=-7n^2 equation:

Simplifying
12 + 31n = -7n2

Solving
12 + 31n = -7n2

Solving for variable 'n'.

Combine like terms: -7n2 + 7n2 = 0
12 + 31n + 7n2 = 0

Factor a trinomial.
(4 + n)(3 + 7n) = 0

Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 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 + n = 0 + -4

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

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

Simplifying
n = -4
Subproblem 2
Set the factor '(3 + 7n)' equal to zero and attempt to solve:

Simplifying
3 + 7n = 0

Solving
3 + 7n = 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 + 7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7n = 0 + -3
7n = 0 + -3

Combine like terms: 0 + -3 = -3
7n = -3

Divide each side by '7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
Solution
n = {-4, -0.4285714286}