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

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

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

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

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

Multiply (8 + n) * (-6 + 5n)
(8(-6 + 5n) + n(-6 + 5n)) = 0
((-6 * 8 + 5n * 8) + n(-6 + 5n)) = 0
((-48 + 40n) + n(-6 + 5n)) = 0
(-48 + 40n + (-6 * n + 5n * n)) = 0
(-48 + 40n + (-6n + 5n2)) = 0

Combine like terms: 40n + -6n = 34n
(-48 + 34n + 5n2) = 0

Solving
-48 + 34n + 5n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 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 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
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 = {-8, 1.2}