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

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

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

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

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

Multiply (4 + x) * (5 + 2x)
(4(5 + 2x) + x(5 + 2x)) = -1
((5 * 4 + 2x * 4) + x(5 + 2x)) = -1
((20 + 8x) + x(5 + 2x)) = -1
(20 + 8x + (5 * x + 2x * x)) = -1
(20 + 8x + (5x + 2x2)) = -1

Combine like terms: 8x + 5x = 13x
(20 + 13x + 2x2) = -1

Solving
20 + 13x + 2x2 = -1

Solving for variable 'x'.

Reorder the terms:
20 + 1 + 13x + 2x2 = -1 + 1

Combine like terms: 20 + 1 = 21
21 + 13x + 2x2 = -1 + 1

Combine like terms: -1 + 1 = 0
21 + 13x + 2x2 = 0

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

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

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

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

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

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

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

Simplifying
x = -3.5
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {-3.5, -3}