(3n-8)(2n-1)=0

Solution for (3n-8)(2n-1)=0 equation:

Simplifying
(3n + -8)(2n + -1) = 0

Reorder the terms:
(-8 + 3n)(2n + -1) = 0

Reorder the terms:
(-8 + 3n)(-1 + 2n) = 0

Multiply (-8 + 3n) * (-1 + 2n)
(-8(-1 + 2n) + 3n * (-1 + 2n)) = 0
((-1 * -8 + 2n * -8) + 3n * (-1 + 2n)) = 0
((8 + -16n) + 3n * (-1 + 2n)) = 0
(8 + -16n + (-1 * 3n + 2n * 3n)) = 0
(8 + -16n + (-3n + 6n2)) = 0

Combine like terms: -16n + -3n = -19n
(8 + -19n + 6n2) = 0

Solving
8 + -19n + 6n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {0.5, 2.666666667}