(n+5)(3n+2)=0

Solution for (n+5)(3n+2)=0 equation:

Simplifying
(n + 5)(3n + 2) = 0

Reorder the terms:
(5 + n)(3n + 2) = 0

Reorder the terms:
(5 + n)(2 + 3n) = 0

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

Combine like terms: 15n + 2n = 17n
(10 + 17n + 3n2) = 0

Solving
10 + 17n + 3n2 = 0

Solving for variable 'n'.

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

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

Simplifying
5 + n = 0

Solving
5 + n = 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 + n = 0 + -5

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

Combine like terms: 0 + -5 = -5
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}