(3a+12)(a-9)=0

Solution for (3a+12)(a-9)=0 equation:

Simplifying
(3a + 12)(a + -9) = 0

Reorder the terms:
(12 + 3a)(a + -9) = 0

Reorder the terms:
(12 + 3a)(-9 + a) = 0

Multiply (12 + 3a) * (-9 + a)
(12(-9 + a) + 3a * (-9 + a)) = 0
((-9 * 12 + a * 12) + 3a * (-9 + a)) = 0
((-108 + 12a) + 3a * (-9 + a)) = 0
(-108 + 12a + (-9 * 3a + a * 3a)) = 0
(-108 + 12a + (-27a + 3a2)) = 0

Combine like terms: 12a + -27a = -15a
(-108 + -15a + 3a2) = 0

Solving
-108 + -15a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + -5a + a2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 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 + -1a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1a = 0 + -9
-1a = 0 + -9

Combine like terms: 0 + -9 = -9
-1a = -9

Divide each side by '-1'.
a = 9

Simplifying
a = 9
Solution
a = {-4, 9}