(4n-3)(2n+1)=0

Solution for (4n-3)(2n+1)=0 equation:

Simplifying
(4n + -3)(2n + 1) = 0

Reorder the terms:
(-3 + 4n)(2n + 1) = 0

Reorder the terms:
(-3 + 4n)(1 + 2n) = 0

Multiply (-3 + 4n) * (1 + 2n)
(-3(1 + 2n) + 4n * (1 + 2n)) = 0
((1 * -3 + 2n * -3) + 4n * (1 + 2n)) = 0
((-3 + -6n) + 4n * (1 + 2n)) = 0
(-3 + -6n + (1 * 4n + 2n * 4n)) = 0
(-3 + -6n + (4n + 8n2)) = 0

Combine like terms: -6n + 4n = -2n
(-3 + -2n + 8n2) = 0

Solving
-3 + -2n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -2n)(3 + -4n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 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 + -4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4n = 0 + -3
-4n = 0 + -3

Combine like terms: 0 + -3 = -3
-4n = -3

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {-0.5, 0.75}