(9a+5)(4a-3)=0

Solution for (9a+5)(4a-3)=0 equation:

Simplifying
(9a + 5)(4a + -3) = 0

Reorder the terms:
(5 + 9a)(4a + -3) = 0

Reorder the terms:
(5 + 9a)(-3 + 4a) = 0

Multiply (5 + 9a) * (-3 + 4a)
(5(-3 + 4a) + 9a * (-3 + 4a)) = 0
((-3 * 5 + 4a * 5) + 9a * (-3 + 4a)) = 0
((-15 + 20a) + 9a * (-3 + 4a)) = 0
(-15 + 20a + (-3 * 9a + 4a * 9a)) = 0
(-15 + 20a + (-27a + 36a2)) = 0

Combine like terms: 20a + -27a = -7a
(-15 + -7a + 36a2) = 0

Solving
-15 + -7a + 36a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -9a)(3 + -4a) = 0

Subproblem 1
Set the factor '(-5 + -9a)' equal to zero and attempt to solve:

Simplifying
-5 + -9a = 0

Solving
-5 + -9a = 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 + -9a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -9a = 0 + 5
-9a = 0 + 5

Combine like terms: 0 + 5 = 5
-9a = 5

Divide each side by '-9'.
a = -0.5555555556

Simplifying
a = -0.5555555556
Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

Solving
3 + -4a = 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 + -4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a = 0 + -3
-4a = 0 + -3

Combine like terms: 0 + -3 = -3
-4a = -3

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Solution
a = {-0.5555555556, 0.75}