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

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

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

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

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

Multiply (1 + 4n) * (-3 + 2n)
(1(-3 + 2n) + 4n * (-3 + 2n)) = 0
((-3 * 1 + 2n * 1) + 4n * (-3 + 2n)) = 0
((-3 + 2n) + 4n * (-3 + 2n)) = 0
(-3 + 2n + (-3 * 4n + 2n * 4n)) = 0
(-3 + 2n + (-12n + 8n2)) = 0

Combine like terms: 2n + -12n = -10n
(-3 + -10n + 8n2) = 0

Solving
-3 + -10n + 8n2 = 0

Solving for variable 'n'.

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

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

Simplifying
3 + -2n = 0

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

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-0.25, 1.5}