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

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

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

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

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

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

Solving
4 + 4n + -3n2 = 0

Solving for variable 'n'.

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

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

Simplifying
2 + -1n = 0

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

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Subproblem 2
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
Solution
n = {2, -0.6666666667}