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

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

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

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

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

Combine like terms: 4 + 1 = 5
(-2 + 3n)(5 + n) = 0

Multiply (-2 + 3n) * (5 + n)
(-2(5 + n) + 3n * (5 + n)) = 0
((5 * -2 + n * -2) + 3n * (5 + n)) = 0
((-10 + -2n) + 3n * (5 + n)) = 0
(-10 + -2n + (5 * 3n + n * 3n)) = 0
(-10 + -2n + (15n + 3n2)) = 0

Combine like terms: -2n + 15n = 13n
(-10 + 13n + 3n2) = 0

Solving
-10 + 13n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -1n)(2 + -3n) = 0

Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
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 = {-5, 0.6666666667}