3n^2+24=22n

Solution for 3n^2+24=22n equation:

Simplifying
3n2 + 24 = 22n

Reorder the terms:
24 + 3n2 = 22n

Solving
24 + 3n2 = 22n

Solving for variable 'n'.

Reorder the terms:
24 + -22n + 3n2 = 22n + -22n

Combine like terms: 22n + -22n = 0
24 + -22n + 3n2 = 0

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

Subproblem 1
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 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 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
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 = {1.333333333, 6}