(a+4)(3a-6)=0

Solution for (a+4)(3a-6)=0 equation:

Simplifying
(a + 4)(3a + -6) = 0

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

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

Multiply (4 + a) * (-6 + 3a)
(4(-6 + 3a) + a(-6 + 3a)) = 0
((-6 * 4 + 3a * 4) + a(-6 + 3a)) = 0
((-24 + 12a) + a(-6 + 3a)) = 0
(-24 + 12a + (-6 * a + 3a * a)) = 0
(-24 + 12a + (-6a + 3a2)) = 0

Combine like terms: 12a + -6a = 6a
(-24 + 6a + 3a2) = 0

Solving
-24 + 6a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 2a + a2) = 0

Factor a trinomial.
3((-4 + -1a)(2 + -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 '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 2

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