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

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

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

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

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

Multiply (2 + 3n) * (-1 + -2n)
(2(-1 + -2n) + 3n * (-1 + -2n)) = 0
((-1 * 2 + -2n * 2) + 3n * (-1 + -2n)) = 0
((-2 + -4n) + 3n * (-1 + -2n)) = 0
(-2 + -4n + (-1 * 3n + -2n * 3n)) = 0
(-2 + -4n + (-3n + -6n2)) = 0

Combine like terms: -4n + -3n = -7n
(-2 + -7n + -6n2) = 0

Solving
-2 + -7n + -6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 7n + 6n2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 3n)' equal to zero and attempt to solve:

Simplifying
2 + 3n = 0

Solving
2 + 3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3n = 0 + -2
3n = 0 + -2

Combine like terms: 0 + -2 = -2
3n = -2

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
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 = {-0.6666666667, -0.5}