(n+5)(6n-1)=0

Solution for (n+5)(6n-1)=0 equation:

Simplifying
(n + 5)(6n + -1) = 0

Reorder the terms:
(5 + n)(6n + -1) = 0

Reorder the terms:
(5 + n)(-1 + 6n) = 0

Multiply (5 + n) * (-1 + 6n)
(5(-1 + 6n) + n(-1 + 6n)) = 0
((-1 * 5 + 6n * 5) + n(-1 + 6n)) = 0
((-5 + 30n) + n(-1 + 6n)) = 0
(-5 + 30n + (-1 * n + 6n * n)) = 0
(-5 + 30n + (-1n + 6n2)) = 0

Combine like terms: 30n + -1n = 29n
(-5 + 29n + 6n2) = 0

Solving
-5 + 29n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -1n)(1 + -6n) = 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 + -6n)' equal to zero and attempt to solve:

Simplifying
1 + -6n = 0

Solving
1 + -6n = 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 + -6n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6n = 0 + -1
-6n = 0 + -1

Combine like terms: 0 + -1 = -1
-6n = -1

Divide each side by '-6'.
n = 0.1666666667

Simplifying
n = 0.1666666667
Solution
n = {-5, 0.1666666667}