3n^2+12=20n

Solution for 3n^2+12=20n equation:

Simplifying
3n2 + 12 = 20n

Reorder the terms:
12 + 3n2 = 20n

Solving
12 + 3n2 = 20n

Solving for variable 'n'.

Reorder the terms:
12 + -20n + 3n2 = 20n + -20n

Combine like terms: 20n + -20n = 0
12 + -20n + 3n2 = 0

Factor a trinomial.
(2 + -3n)(6 + -1n) = 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 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

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