(3n+2)(2n-12)=0

Solution for (3n+2)(2n-12)=0 equation:

Simplifying
(3n + 2)(2n + -12) = 0

Reorder the terms:
(2 + 3n)(2n + -12) = 0

Reorder the terms:
(2 + 3n)(-12 + 2n) = 0

Multiply (2 + 3n) * (-12 + 2n)
(2(-12 + 2n) + 3n * (-12 + 2n)) = 0
((-12 * 2 + 2n * 2) + 3n * (-12 + 2n)) = 0
((-24 + 4n) + 3n * (-12 + 2n)) = 0
(-24 + 4n + (-12 * 3n + 2n * 3n)) = 0
(-24 + 4n + (-36n + 6n2)) = 0

Combine like terms: 4n + -36n = -32n
(-24 + -32n + 6n2) = 0

Solving
-24 + -32n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -16n + 3n2) = 0

Factor a trinomial.
2((-2 + -3n)(6 + -1n)) = 0

Ignore the factor 2.
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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-0.6666666667, 6}