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

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

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

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

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

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

Combine like terms: -12n + 2n = -10n
4(-3 + -10n + 8n2) = 0
(-3 * 4 + -10n * 4 + 8n2 * 4) = 0
(-12 + -40n + 32n2) = 0

Solving
-12 + -40n + 32n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -10n + 8n2) = 0

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

Ignore the factor 4.
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}