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

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

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

Reorder the terms:
-2(-1 + 3n)(2n + 1) = 0

Reorder the terms:
-2(-1 + 3n)(1 + 2n) = 0

Multiply (-1 + 3n) * (1 + 2n)
-2(-1(1 + 2n) + 3n * (1 + 2n)) = 0
-2((1 * -1 + 2n * -1) + 3n * (1 + 2n)) = 0
-2((-1 + -2n) + 3n * (1 + 2n)) = 0
-2(-1 + -2n + (1 * 3n + 2n * 3n)) = 0
-2(-1 + -2n + (3n + 6n2)) = 0

Combine like terms: -2n + 3n = 1n
-2(-1 + 1n + 6n2) = 0
(-1 * -2 + 1n * -2 + 6n2 * -2) = 0
(2 + -2n + -12n2) = 0

Solving
2 + -2n + -12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -1n + -6n2) = 0

Factor a trinomial.
2((1 + -3n)(1 + 2n)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Solution
n = {0.3333333333, -0.5}