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

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

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

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

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

Multiply (5 + 2a) * (1 + a)
(5(1 + a) + 2a * (1 + a)) = -1
((1 * 5 + a * 5) + 2a * (1 + a)) = -1
((5 + 5a) + 2a * (1 + a)) = -1
(5 + 5a + (1 * 2a + a * 2a)) = -1
(5 + 5a + (2a + 2a2)) = -1

Combine like terms: 5a + 2a = 7a
(5 + 7a + 2a2) = -1

Solving
5 + 7a + 2a2 = -1

Solving for variable 'a'.

Reorder the terms:
5 + 1 + 7a + 2a2 = -1 + 1

Combine like terms: 5 + 1 = 6
6 + 7a + 2a2 = -1 + 1

Combine like terms: -1 + 1 = 0
6 + 7a + 2a2 = 0

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

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

Simplifying
2 + a = 0

Solving
2 + a = 0

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

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

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

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

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

Simplifying
3 + 2a = 0

Solving
3 + 2a = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2a = 0 + -3

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

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

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

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