3n^2-33n=-72

Solution for 3n^2-33n=-72 equation:

Simplifying
3n2 + -33n = -72

Reorder the terms:
-33n + 3n2 = -72

Solving
-33n + 3n2 = -72

Solving for variable 'n'.

Reorder the terms:
72 + -33n + 3n2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + -33n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + -11n + n2) = 0

Factor a trinomial.
3((3 + -1n)(8 + -1n)) = 0

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

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {3, 8}