a(2a+5)=-3

Solution for a(2a+5)=-3 equation:

Simplifying
a(2a + 5) = -3

Reorder the terms:
a(5 + 2a) = -3
(5 * a + 2a * a) = -3
(5a + 2a2) = -3

Solving
5a + 2a2 = -3

Solving for variable 'a'.

Reorder the terms:
3 + 5a + 2a2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 5a + 2a2 = 0

Factor a trinomial.
(3 + 2a)(1 + a) = 0

Subproblem 1
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
Subproblem 2
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
Solution
a = {-1.5, -1}