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

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

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

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

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

Multiply (5 + 2n) * (3 + 2n)
(5(3 + 2n) + 2n * (3 + 2n)) = 0
((3 * 5 + 2n * 5) + 2n * (3 + 2n)) = 0
((15 + 10n) + 2n * (3 + 2n)) = 0
(15 + 10n + (3 * 2n + 2n * 2n)) = 0
(15 + 10n + (6n + 4n2)) = 0

Combine like terms: 10n + 6n = 16n
(15 + 16n + 4n2) = 0

Solving
15 + 16n + 4n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(5 + 2n)' equal to zero and attempt to solve:

Simplifying
5 + 2n = 0

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

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

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

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
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 = {-2.5, -1.5}