(3n-1)(n+5)=0

Solution for (3n-1)(n+5)=0 equation:

Simplifying
(3n + -1)(n + 5) = 0

Reorder the terms:
(-1 + 3n)(n + 5) = 0

Reorder the terms:
(-1 + 3n)(5 + n) = 0

Multiply (-1 + 3n) * (5 + n)
(-1(5 + n) + 3n * (5 + n)) = 0
((5 * -1 + n * -1) + 3n * (5 + n)) = 0
((-5 + -1n) + 3n * (5 + n)) = 0
(-5 + -1n + (5 * 3n + n * 3n)) = 0
(-5 + -1n + (15n + 3n2)) = 0

Combine like terms: -1n + 15n = 14n
(-5 + 14n + 3n2) = 0

Solving
-5 + 14n + 3n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 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 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-5, 0.3333333333}