3n^2=-n

Solution for 3n^2=-n equation:

Simplifying
3n2 = -1n

Solving
3n2 = -1n

Solving for variable 'n'.

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

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

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

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(1 + 3n)' equal to zero and attempt to solve:

Simplifying
1 + 3n = 0

Solving
1 + 3n = 0

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

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

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

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

Divide each side by '3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Solution
n = {0, -0.3333333333}