(2n+5)(n+4)=-1

Solution for (2n+5)(n+4)=-1 equation:

Simplifying
(2n + 5)(n + 4) = -1

Reorder the terms:
(5 + 2n)(n + 4) = -1

Reorder the terms:
(5 + 2n)(4 + n) = -1

Multiply (5 + 2n) * (4 + n)
(5(4 + n) + 2n * (4 + n)) = -1
((4 * 5 + n * 5) + 2n * (4 + n)) = -1
((20 + 5n) + 2n * (4 + n)) = -1
(20 + 5n + (4 * 2n + n * 2n)) = -1
(20 + 5n + (8n + 2n2)) = -1

Combine like terms: 5n + 8n = 13n
(20 + 13n + 2n2) = -1

Solving
20 + 13n + 2n2 = -1

Solving for variable 'n'.

Reorder the terms:
20 + 1 + 13n + 2n2 = -1 + 1

Combine like terms: 20 + 1 = 21
21 + 13n + 2n2 = -1 + 1

Combine like terms: -1 + 1 = 0
21 + 13n + 2n2 = 0

Factor a trinomial.
(7 + 2n)(3 + n) = 0

Subproblem 1
Set the factor '(7 + 2n)' equal to zero and attempt to solve:

Simplifying
7 + 2n = 0

Solving
7 + 2n = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2n = 0 + -7
2n = 0 + -7

Combine like terms: 0 + -7 = -7
2n = -7

Divide each side by '2'.
n = -3.5

Simplifying
n = -3.5
Subproblem 2
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
Solution
n = {-3.5, -3}