(n-6)(5n+8)=0

Solution for (n-6)(5n+8)=0 equation:

Simplifying
(n + -6)(5n + 8) = 0

Reorder the terms:
(-6 + n)(5n + 8) = 0

Reorder the terms:
(-6 + n)(8 + 5n) = 0

Multiply (-6 + n) * (8 + 5n)
(-6(8 + 5n) + n(8 + 5n)) = 0
((8 * -6 + 5n * -6) + n(8 + 5n)) = 0
((-48 + -30n) + n(8 + 5n)) = 0
(-48 + -30n + (8 * n + 5n * n)) = 0
(-48 + -30n + (8n + 5n2)) = 0

Combine like terms: -30n + 8n = -22n
(-48 + -22n + 5n2) = 0

Solving
-48 + -22n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-8 + -5n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -5n)' equal to zero and attempt to solve:

Simplifying
-8 + -5n = 0

Solving
-8 + -5n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5n = 0 + 8
-5n = 0 + 8

Combine like terms: 0 + 8 = 8
-5n = 8

Divide each side by '-5'.
n = -1.6

Simplifying
n = -1.6
Subproblem 2
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
Solution
n = {-1.6, 6}