(5n-4)(n+6)=0

Solution for (5n-4)(n+6)=0 equation:

Simplifying
(5n + -4)(n + 6) = 0

Reorder the terms:
(-4 + 5n)(n + 6) = 0

Reorder the terms:
(-4 + 5n)(6 + n) = 0

Multiply (-4 + 5n) * (6 + n)
(-4(6 + n) + 5n * (6 + n)) = 0
((6 * -4 + n * -4) + 5n * (6 + n)) = 0
((-24 + -4n) + 5n * (6 + n)) = 0
(-24 + -4n + (6 * 5n + n * 5n)) = 0
(-24 + -4n + (30n + 5n2)) = 0

Combine like terms: -4n + 30n = 26n
(-24 + 26n + 5n2) = 0

Solving
-24 + 26n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -1n)(4 + -5n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -5n)' equal to zero and attempt to solve:

Simplifying
4 + -5n = 0

Solving
4 + -5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5n = 0 + -4
-5n = 0 + -4

Combine like terms: 0 + -4 = -4
-5n = -4

Divide each side by '-5'.
n = 0.8

Simplifying
n = 0.8
Solution
n = {-6, 0.8}