a(2a+3)=-1

Solution for a(2a+3)=-1 equation:

Simplifying
a(2a + 3) = -1

Reorder the terms:
a(3 + 2a) = -1
(3 * a + 2a * a) = -1
(3a + 2a2) = -1

Solving
3a + 2a2 = -1

Solving for variable 'a'.

Reorder the terms:
1 + 3a + 2a2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 3a + 2a2 = 0

Factor a trinomial.
(1 + a)(1 + 2a) = 0

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

Simplifying
1 + a = 0

Solving
1 + a = 0

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

Add '-1' to each side of the equation.
1 + -1 + a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

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

Simplifying
1 + 2a = 0

Solving
1 + 2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-1, -0.5}