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

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

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

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

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

Multiply (-3 + n) * (-8 + 3n)
(-3(-8 + 3n) + n(-8 + 3n)) = 0
((-8 * -3 + 3n * -3) + n(-8 + 3n)) = 0
((24 + -9n) + n(-8 + 3n)) = 0
(24 + -9n + (-8 * n + 3n * n)) = 0
(24 + -9n + (-8n + 3n2)) = 0

Combine like terms: -9n + -8n = -17n
(24 + -17n + 3n2) = 0

Solving
24 + -17n + 3n2 = 0

Solving for variable 'n'.

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

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}