(8n+1)(6n-3)=0

Solution for (8n+1)(6n-3)=0 equation:

Simplifying
(8n + 1)(6n + -3) = 0

Reorder the terms:
(1 + 8n)(6n + -3) = 0

Reorder the terms:
(1 + 8n)(-3 + 6n) = 0

Multiply (1 + 8n) * (-3 + 6n)
(1(-3 + 6n) + 8n * (-3 + 6n)) = 0
((-3 * 1 + 6n * 1) + 8n * (-3 + 6n)) = 0
((-3 + 6n) + 8n * (-3 + 6n)) = 0
(-3 + 6n + (-3 * 8n + 6n * 8n)) = 0
(-3 + 6n + (-24n + 48n2)) = 0

Combine like terms: 6n + -24n = -18n
(-3 + -18n + 48n2) = 0

Solving
-3 + -18n + 48n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -6n + 16n2) = 0

Factor a trinomial.
3((-1 + -8n)(1 + -2n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -8n)' equal to zero and attempt to solve:

Simplifying
-1 + -8n = 0

Solving
-1 + -8n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -8n = 0 + 1

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

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

Divide each side by '-8'.
n = -0.125

Simplifying
n = -0.125
Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {-0.125, 0.5}