12-3n^2=16n

Solution for 12-3n^2=16n equation:

Simplifying
12 + -3n2 = 16n

Solving
12 + -3n2 = 16n

Solving for variable 'n'.

Reorder the terms:
12 + -16n + -3n2 = 16n + -16n

Combine like terms: 16n + -16n = 0
12 + -16n + -3n2 = 0

Factor a trinomial.
(2 + -3n)(6 + n) = 0

Subproblem 1
Set the factor '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3n = 0 + -2

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

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

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Subproblem 2
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Solution
n = {0.6666666667, -6}