(3n-5)(n-6)=0

Solution for (3n-5)(n-6)=0 equation:

Simplifying
(3n + -5)(n + -6) = 0

Reorder the terms:
(-5 + 3n)(n + -6) = 0

Reorder the terms:
(-5 + 3n)(-6 + n) = 0

Multiply (-5 + 3n) * (-6 + n)
(-5(-6 + n) + 3n * (-6 + n)) = 0
((-6 * -5 + n * -5) + 3n * (-6 + n)) = 0
((30 + -5n) + 3n * (-6 + n)) = 0
(30 + -5n + (-6 * 3n + n * 3n)) = 0
(30 + -5n + (-18n + 3n2)) = 0

Combine like terms: -5n + -18n = -23n
(30 + -23n + 3n2) = 0

Solving
30 + -23n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + -3n)(6 + -1n) = 0

Subproblem 1
Set the factor '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
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 = {1.666666667, 6}