3(3n^2+2n-1)=0

Solution for 3(3n^2+2n-1)=0 equation:

Simplifying
3(3n2 + 2n + -1) = 0

Reorder the terms:
3(-1 + 2n + 3n2) = 0
(-1 * 3 + 2n * 3 + 3n2 * 3) = 0
(-3 + 6n + 9n2) = 0

Solving
-3 + 6n + 9n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2n + 3n2) = 0

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

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 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 + -1n = 0 + 1

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

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

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

Simplifying
n = -1
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 = {-1, 0.3333333333}