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

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

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

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

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

Multiply (-3 + 5n) * (3 + 8n)
(-3(3 + 8n) + 5n * (3 + 8n)) = 0
((3 * -3 + 8n * -3) + 5n * (3 + 8n)) = 0
((-9 + -24n) + 5n * (3 + 8n)) = 0
(-9 + -24n + (3 * 5n + 8n * 5n)) = 0
(-9 + -24n + (15n + 40n2)) = 0

Combine like terms: -24n + 15n = -9n
(-9 + -9n + 40n2) = 0

Solving
-9 + -9n + 40n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -8n)(3 + -5n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -5n)' equal to zero and attempt to solve:

Simplifying
3 + -5n = 0

Solving
3 + -5n = 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 + -5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5n = 0 + -3
-5n = 0 + -3

Combine like terms: 0 + -3 = -3
-5n = -3

Divide each side by '-5'.
n = 0.6

Simplifying
n = 0.6
Solution
n = {-0.375, 0.6}