(9a-5)(6a+3)=

Solution for (9a-5)(6a+3)= equation:

Simplifying
(9a + -5)(6a + 3) = 0

Reorder the terms:
(-5 + 9a)(6a + 3) = 0

Reorder the terms:
(-5 + 9a)(3 + 6a) = 0

Multiply (-5 + 9a) * (3 + 6a)
(-5(3 + 6a) + 9a * (3 + 6a)) = 0
((3 * -5 + 6a * -5) + 9a * (3 + 6a)) = 0
((-15 + -30a) + 9a * (3 + 6a)) = 0
(-15 + -30a + (3 * 9a + 6a * 9a)) = 0
(-15 + -30a + (27a + 54a2)) = 0

Combine like terms: -30a + 27a = -3a
(-15 + -3a + 54a2) = 0

Solving
-15 + -3a + 54a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -1a + 18a2) = 0

Factor a trinomial.
3((-1 + -2a)(5 + -9a)) = 0

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 2
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
Solution
a = {-0.5, 0.5555555556}