12n^2+48=80n

Solution for 12n^2+48=80n equation:

Simplifying
12n2 + 48 = 80n

Reorder the terms:
48 + 12n2 = 80n

Solving
48 + 12n2 = 80n

Solving for variable 'n'.

Reorder the terms:
48 + -80n + 12n2 = 80n + -80n

Combine like terms: 80n + -80n = 0
48 + -80n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + -20n + 3n2) = 0

Factor a trinomial.
4((2 + -3n)(6 + -1n)) = 0

Ignore the factor 4.
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}