(a+2)(5a+3)=0

Solution for (a+2)(5a+3)=0 equation:

Simplifying
(a + 2)(5a + 3) = 0

Reorder the terms:
(2 + a)(5a + 3) = 0

Reorder the terms:
(2 + a)(3 + 5a) = 0

Multiply (2 + a) * (3 + 5a)
(2(3 + 5a) + a(3 + 5a)) = 0
((3 * 2 + 5a * 2) + a(3 + 5a)) = 0
((6 + 10a) + a(3 + 5a)) = 0
(6 + 10a + (3 * a + 5a * a)) = 0
(6 + 10a + (3a + 5a2)) = 0

Combine like terms: 10a + 3a = 13a
(6 + 13a + 5a2) = 0

Solving
6 + 13a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + a)(3 + 5a) = 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 + 5a)' equal to zero and attempt to solve:

Simplifying
3 + 5a = 0

Solving
3 + 5a = 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 + 5a = 0 + -3

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

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

Divide each side by '5'.
a = -0.6

Simplifying
a = -0.6
Solution
a = {-2, -0.6}