(9a+5)(4a-12)=0

Solution for (9a+5)(4a-12)=0 equation:

Simplifying
(9a + 5)(4a + -12) = 0

Reorder the terms:
(5 + 9a)(4a + -12) = 0

Reorder the terms:
(5 + 9a)(-12 + 4a) = 0

Multiply (5 + 9a) * (-12 + 4a)
(5(-12 + 4a) + 9a * (-12 + 4a)) = 0
((-12 * 5 + 4a * 5) + 9a * (-12 + 4a)) = 0
((-60 + 20a) + 9a * (-12 + 4a)) = 0
(-60 + 20a + (-12 * 9a + 4a * 9a)) = 0
(-60 + 20a + (-108a + 36a2)) = 0

Combine like terms: 20a + -108a = -88a
(-60 + -88a + 36a2) = 0

Solving
-60 + -88a + 36a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -22a + 9a2) = 0

Factor a trinomial.
4((-5 + -9a)(3 + -1a)) = 0

Ignore the factor 4.
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 + -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 = {-0.5555555556, 3}