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

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

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

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

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

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

Combine like terms: 5x + 2x = 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}