(2n+5)(n+4)=0

Solution for (2n+5)(n+4)=0 equation:

Simplifying
(2n + 5)(n + 4) = 0

Reorder the terms:
(5 + 2n)(n + 4) = 0

Reorder the terms:
(5 + 2n)(4 + n) = 0

Multiply (5 + 2n) * (4 + n)
(5(4 + n) + 2n * (4 + n)) = 0
((4 * 5 + n * 5) + 2n * (4 + n)) = 0
((20 + 5n) + 2n * (4 + n)) = 0
(20 + 5n + (4 * 2n + n * 2n)) = 0
(20 + 5n + (8n + 2n2)) = 0

Combine like terms: 5n + 8n = 13n
(20 + 13n + 2n2) = 0

Solving
20 + 13n + 2n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Subproblem 2
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
Solution
n = {-4, -2.5}