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

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

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

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

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

Multiply (3 + n) * (2 + 5n)
(3(2 + 5n) + n(2 + 5n)) = 0
((2 * 3 + 5n * 3) + n(2 + 5n)) = 0
((6 + 15n) + n(2 + 5n)) = 0
(6 + 15n + (2 * n + 5n * n)) = 0
(6 + 15n + (2n + 5n2)) = 0

Combine like terms: 15n + 2n = 17n
(6 + 17n + 5n2) = 0

Solving
6 + 17n + 5n2 = 0

Solving for variable 'n'.

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

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

Simplifying
3 + n = 0

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

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

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

Simplifying
n = -3
Subproblem 2
Set the factor '(2 + 5n)' equal to zero and attempt to solve:

Simplifying
2 + 5n = 0

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

Combine like terms: 2 + -2 = 0
0 + 5n = 0 + -2
5n = 0 + -2

Combine like terms: 0 + -2 = -2
5n = -2

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {-3, -0.4}