(15a+9)(4a+5)=0

Solution for (15a+9)(4a+5)=0 equation:

Simplifying
(15a + 9)(4a + 5) = 0

Reorder the terms:
(9 + 15a)(4a + 5) = 0

Reorder the terms:
(9 + 15a)(5 + 4a) = 0

Multiply (9 + 15a) * (5 + 4a)
(9(5 + 4a) + 15a * (5 + 4a)) = 0
((5 * 9 + 4a * 9) + 15a * (5 + 4a)) = 0
((45 + 36a) + 15a * (5 + 4a)) = 0
(45 + 36a + (5 * 15a + 4a * 15a)) = 0
(45 + 36a + (75a + 60a2)) = 0

Combine like terms: 36a + 75a = 111a
(45 + 111a + 60a2) = 0

Solving
45 + 111a + 60a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 37a + 20a2) = 0

Factor a trinomial.
3((5 + 4a)(3 + 5a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 4a)' equal to zero and attempt to solve:

Simplifying
5 + 4a = 0

Solving
5 + 4a = 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 + 4a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4a = 0 + -5
4a = 0 + -5

Combine like terms: 0 + -5 = -5
4a = -5

Divide each side by '4'.
a = -1.25

Simplifying
a = -1.25
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 = {-1.25, -0.6}