0=3n^2+n-2914

Solution for 0=3n^2+n-2914 equation:

Simplifying
0 = 3n2 + n + -2914

Reorder the terms:
0 = -2914 + n + 3n2

Solving
0 = -2914 + n + 3n2

Solving for variable 'n'.

Combine like terms: 0 + 2914 = 2914
2914 + -1n + -3n2 = -2914 + n + 3n2 + 2914 + -1n + -3n2

Reorder the terms:
2914 + -1n + -3n2 = -2914 + 2914 + n + -1n + 3n2 + -3n2

Combine like terms: -2914 + 2914 = 0
2914 + -1n + -3n2 = 0 + n + -1n + 3n2 + -3n2
2914 + -1n + -3n2 = n + -1n + 3n2 + -3n2

Combine like terms: n + -1n = 0
2914 + -1n + -3n2 = 0 + 3n2 + -3n2
2914 + -1n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
2914 + -1n + -3n2 = 0

Factor a trinomial.
(31 + -1n)(94 + 3n) = 0

Subproblem 1
Set the factor '(31 + -1n)' equal to zero and attempt to solve:

Simplifying
31 + -1n = 0

Solving
31 + -1n = 0

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

Add '-31' to each side of the equation.
31 + -31 + -1n = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -1n = 0 + -31
-1n = 0 + -31

Combine like terms: 0 + -31 = -31
-1n = -31

Divide each side by '-1'.
n = 31

Simplifying
n = 31
Subproblem 2
Set the factor '(94 + 3n)' equal to zero and attempt to solve:

Simplifying
94 + 3n = 0

Solving
94 + 3n = 0

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

Add '-94' to each side of the equation.
94 + -94 + 3n = 0 + -94

Combine like terms: 94 + -94 = 0
0 + 3n = 0 + -94
3n = 0 + -94

Combine like terms: 0 + -94 = -94
3n = -94

Divide each side by '3'.
n = -31.33333333

Simplifying
n = -31.33333333
Solution
n = {31, -31.33333333}