36=24N-3N^2

Solution for 36=24N-3N^2 equation:

Simplifying
36 = 24N + -3N2

Solving
36 = 24N + -3N2

Solving for variable 'N'.

Reorder the terms:
36 + -24N + 3N2 = 24N + -24N + -3N2 + 3N2

Combine like terms: 24N + -24N = 0
36 + -24N + 3N2 = 0 + -3N2 + 3N2
36 + -24N + 3N2 = -3N2 + 3N2

Combine like terms: -3N2 + 3N2 = 0
36 + -24N + 3N2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -8N + N2) = 0

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

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

Simplifying
2 + -1N = 0

Solving
2 + -1N = 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 + -1N = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1N = 0 + -2
-1N = 0 + -2

Combine like terms: 0 + -2 = -2
-1N = -2

Divide each side by '-1'.
N = 2

Simplifying
N = 2
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 = {2, 6}