(3a-12)(a+5)=0

Solution for (3a-12)(a+5)=0 equation:

Simplifying
(3a + -12)(a + 5) = 0

Reorder the terms:
(-12 + 3a)(a + 5) = 0

Reorder the terms:
(-12 + 3a)(5 + a) = 0

Multiply (-12 + 3a) * (5 + a)
(-12(5 + a) + 3a * (5 + a)) = 0
((5 * -12 + a * -12) + 3a * (5 + a)) = 0
((-60 + -12a) + 3a * (5 + a)) = 0
(-60 + -12a + (5 * 3a + a * 3a)) = 0
(-60 + -12a + (15a + 3a2)) = 0

Combine like terms: -12a + 15a = 3a
(-60 + 3a + 3a2) = 0

Solving
-60 + 3a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + a + a2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 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 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
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
Solution
a = {-5, 4}