(4n-1)(8n+3)=0

Solution for (4n-1)(8n+3)=0 equation:

Simplifying
(4n + -1)(8n + 3) = 0

Reorder the terms:
(-1 + 4n)(8n + 3) = 0

Reorder the terms:
(-1 + 4n)(3 + 8n) = 0

Multiply (-1 + 4n) * (3 + 8n)
(-1(3 + 8n) + 4n * (3 + 8n)) = 0
((3 * -1 + 8n * -1) + 4n * (3 + 8n)) = 0
((-3 + -8n) + 4n * (3 + 8n)) = 0
(-3 + -8n + (3 * 4n + 8n * 4n)) = 0
(-3 + -8n + (12n + 32n2)) = 0

Combine like terms: -8n + 12n = 4n
(-3 + 4n + 32n2) = 0

Solving
-3 + 4n + 32n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -8n)(1 + -4n) = 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 '(1 + -4n)' equal to zero and attempt to solve:

Simplifying
1 + -4n = 0

Solving
1 + -4n = 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 + -4n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4n = 0 + -1
-4n = 0 + -1

Combine like terms: 0 + -1 = -1
-4n = -1

Divide each side by '-4'.
n = 0.25

Simplifying
n = 0.25
Solution
n = {-0.375, 0.25}