331=3n^2-3n+1

Solution for 331=3n^2-3n+1 equation:

Simplifying
331 = 3n2 + -3n + 1

Reorder the terms:
331 = 1 + -3n + 3n2

Solving
331 = 1 + -3n + 3n2

Solving for variable 'n'.

Combine like terms: 331 + -1 = 330
330 + 3n + -3n2 = 1 + -3n + 3n2 + -1 + 3n + -3n2

Reorder the terms:
330 + 3n + -3n2 = 1 + -1 + -3n + 3n + 3n2 + -3n2

Combine like terms: 1 + -1 = 0
330 + 3n + -3n2 = 0 + -3n + 3n + 3n2 + -3n2
330 + 3n + -3n2 = -3n + 3n + 3n2 + -3n2

Combine like terms: -3n + 3n = 0
330 + 3n + -3n2 = 0 + 3n2 + -3n2
330 + 3n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
330 + 3n + -3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(110 + n + -1n2) = 0

Factor a trinomial.
3((11 + -1n)(10 + n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Subproblem 2
Set the factor '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 0

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

Add '-10' to each side of the equation.
10 + -10 + n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + n = 0 + -10
n = 0 + -10

Combine like terms: 0 + -10 = -10
n = -10

Simplifying
n = -10
Solution
n = {11, -10}