(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 = 1n
(-2 + 1n + 6n2) = 0

Solving
-2 + 1n + 6n2 = 0

Solving for variable 'n'.

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

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}