(8n-3)(5n+6)=0

Solution for (8n-3)(5n+6)=0 equation:

Simplifying
(8n + -3)(5n + 6) = 0

Reorder the terms:
(-3 + 8n)(5n + 6) = 0

Reorder the terms:
(-3 + 8n)(6 + 5n) = 0

Multiply (-3 + 8n) * (6 + 5n)
(-3(6 + 5n) + 8n * (6 + 5n)) = 0
((6 * -3 + 5n * -3) + 8n * (6 + 5n)) = 0
((-18 + -15n) + 8n * (6 + 5n)) = 0
(-18 + -15n + (6 * 8n + 5n * 8n)) = 0
(-18 + -15n + (48n + 40n2)) = 0

Combine like terms: -15n + 48n = 33n
(-18 + 33n + 40n2) = 0

Solving
-18 + 33n + 40n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -5n)(3 + -8n) = 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 '(3 + -8n)' equal to zero and attempt to solve:

Simplifying
3 + -8n = 0

Solving
3 + -8n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -8n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8n = 0 + -3
-8n = 0 + -3

Combine like terms: 0 + -3 = -3
-8n = -3

Divide each side by '-8'.
n = 0.375

Simplifying
n = 0.375
Solution
n = {-1.2, 0.375}