(5a-9)(10a+6)=0

Solution for (5a-9)(10a+6)=0 equation:

Simplifying
(5a + -9)(10a + 6) = 0

Reorder the terms:
(-9 + 5a)(10a + 6) = 0

Reorder the terms:
(-9 + 5a)(6 + 10a) = 0

Multiply (-9 + 5a) * (6 + 10a)
(-9(6 + 10a) + 5a * (6 + 10a)) = 0
((6 * -9 + 10a * -9) + 5a * (6 + 10a)) = 0
((-54 + -90a) + 5a * (6 + 10a)) = 0
(-54 + -90a + (6 * 5a + 10a * 5a)) = 0
(-54 + -90a + (30a + 50a2)) = 0

Combine like terms: -90a + 30a = -60a
(-54 + -60a + 50a2) = 0

Solving
-54 + -60a + 50a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -30a + 25a2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(9 + -5a)' equal to zero and attempt to solve:

Simplifying
9 + -5a = 0

Solving
9 + -5a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5a = 0 + -9

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

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

Divide each side by '-5'.
a = 1.8

Simplifying
a = 1.8
Solution
a = {-0.6, 1.8}