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

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

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

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

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

Multiply (5 + 6n) * (-6 + 5n)
(5(-6 + 5n) + 6n * (-6 + 5n)) = 0
((-6 * 5 + 5n * 5) + 6n * (-6 + 5n)) = 0
((-30 + 25n) + 6n * (-6 + 5n)) = 0
(-30 + 25n + (-6 * 6n + 5n * 6n)) = 0
(-30 + 25n + (-36n + 30n2)) = 0

Combine like terms: 25n + -36n = -11n
(-30 + -11n + 30n2) = 0

Solving
-30 + -11n + 30n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-5 + -6n = 0

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

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

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

Divide each side by '-6'.
n = -0.8333333333

Simplifying
n = -0.8333333333
Subproblem 2
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
Solution
n = {-0.8333333333, 1.2}