22n-(3n^2)=24

Solution for 22n-(3n^2)=24 equation:

Simplifying
22n + -1(3n2) = 24

Remove parenthesis around (3n2)
22n + -1 * 3n2 = 24

Multiply -1 * 3
22n + -3n2 = 24

Solving
22n + -3n2 = 24

Solving for variable 'n'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {6, 1.333333333}