(3n+8)(2n-6)=0

Solution for (3n+8)(2n-6)=0 equation:

Simplifying
(3n + 8)(2n + -6) = 0

Reorder the terms:
(8 + 3n)(2n + -6) = 0

Reorder the terms:
(8 + 3n)(-6 + 2n) = 0

Multiply (8 + 3n) * (-6 + 2n)
(8(-6 + 2n) + 3n * (-6 + 2n)) = 0
((-6 * 8 + 2n * 8) + 3n * (-6 + 2n)) = 0
((-48 + 16n) + 3n * (-6 + 2n)) = 0
(-48 + 16n + (-6 * 3n + 2n * 3n)) = 0
(-48 + 16n + (-18n + 6n2)) = 0

Combine like terms: 16n + -18n = -2n
(-48 + -2n + 6n2) = 0

Solving
-48 + -2n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -1n + 3n2) = 0

Factor a trinomial.
2((-8 + -3n)(3 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve:

Simplifying
-8 + -3n = 0

Solving
-8 + -3n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3n = 0 + 8
-3n = 0 + 8

Combine like terms: 0 + 8 = 8
-3n = 8

Divide each side by '-3'.
n = -2.666666667

Simplifying
n = -2.666666667
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-2.666666667, 3}