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

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

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

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

Multiply (5 + a) * (3 + 5a)
(5(3 + 5a) + a(3 + 5a)) = 0
((3 * 5 + 5a * 5) + a(3 + 5a)) = 0
((15 + 25a) + a(3 + 5a)) = 0
(15 + 25a + (3 * a + 5a * a)) = 0
(15 + 25a + (3a + 5a2)) = 0

Combine like terms: 25a + 3a = 28a
(15 + 28a + 5a2) = 0

Solving
15 + 28a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + a)(3 + 5a) = 0

Subproblem 1
Set the factor '(5 + a)' equal to zero and attempt to solve:

Simplifying
5 + a = 0

Solving
5 + a = 0

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

Add '-5' to each side of the equation.
5 + -5 + a = 0 + -5

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

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

Simplifying
a = -5
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 = {-5, -0.6}