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

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

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

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

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

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

Combine like terms: 2x + 5x = 7x
(5 + 7x + 2x2) = -1

Solving
5 + 7x + 2x2 = -1

Solving for variable 'x'.

Reorder the terms:
5 + 1 + 7x + 2x2 = -1 + 1

Combine like terms: 5 + 1 = 6
6 + 7x + 2x2 = -1 + 1

Combine like terms: -1 + 1 = 0
6 + 7x + 2x2 = 0

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-2, -1.5}