(8a+5)(3a-9)=0

Solution for (8a+5)(3a-9)=0 equation:

Simplifying
(8a + 5)(3a + -9) = 0

Reorder the terms:
(5 + 8a)(3a + -9) = 0

Reorder the terms:
(5 + 8a)(-9 + 3a) = 0

Multiply (5 + 8a) * (-9 + 3a)
(5(-9 + 3a) + 8a * (-9 + 3a)) = 0
((-9 * 5 + 3a * 5) + 8a * (-9 + 3a)) = 0
((-45 + 15a) + 8a * (-9 + 3a)) = 0
(-45 + 15a + (-9 * 8a + 3a * 8a)) = 0
(-45 + 15a + (-72a + 24a2)) = 0

Combine like terms: 15a + -72a = -57a
(-45 + -57a + 24a2) = 0

Solving
-45 + -57a + 24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -19a + 8a2) = 0

Factor a trinomial.
3((-5 + -8a)(3 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -8a)' equal to zero and attempt to solve:

Simplifying
-5 + -8a = 0

Solving
-5 + -8a = 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 + -8a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8a = 0 + 5
-8a = 0 + 5

Combine like terms: 0 + 5 = 5
-8a = 5

Divide each side by '-8'.
a = -0.625

Simplifying
a = -0.625
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

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

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

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.625, 3}