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

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

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

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

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

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

Combine like terms: -8n + 3n = -5n
(-2 + -5n + 12n2) = 0

Solving
-2 + -5n + 12n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -4n)(2 + -3n) = 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 '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3n = 0 + -2

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

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

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Solution
n = {-0.25, 0.6666666667}