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

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

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

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

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

Multiply (-1 + 6n) * (6 + 5n)
(-1(6 + 5n) + 6n * (6 + 5n)) = 0
((6 * -1 + 5n * -1) + 6n * (6 + 5n)) = 0
((-6 + -5n) + 6n * (6 + 5n)) = 0
(-6 + -5n + (6 * 6n + 5n * 6n)) = 0
(-6 + -5n + (36n + 30n2)) = 0

Combine like terms: -5n + 36n = 31n
(-6 + 31n + 30n2) = 0

Solving
-6 + 31n + 30n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(-6 + -5n)' equal to zero and attempt to solve:

Simplifying
-6 + -5n = 0

Solving
-6 + -5n = 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 + -5n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5n = 0 + 6
-5n = 0 + 6

Combine like terms: 0 + 6 = 6
-5n = 6

Divide each side by '-5'.
n = -1.2

Simplifying
n = -1.2
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 = {-1.2, 0.1666666667}