3((-6+-1a)(3+-1a))=0

Solution for 3((-6+-1a)(3+-1a))=0 equation:

Simplifying
3((-6 + -1a)(3 + -1a)) = 0

Multiply (-6 + -1a) * (3 + -1a)
3((-6(3 + -1a) + -1a * (3 + -1a))) = 0
3(((3 * -6 + -1a * -6) + -1a * (3 + -1a))) = 0
3(((-18 + 6a) + -1a * (3 + -1a))) = 0
3((-18 + 6a + (3 * -1a + -1a * -1a))) = 0
3((-18 + 6a + (-3a + 1a2))) = 0

Combine like terms: 6a + -3a = 3a
3((-18 + 3a + 1a2)) = 0
(-18 * 3 + 3a * 3 + 1a2 * 3) = 0
(-54 + 9a + 3a2) = 0

Solving
-54 + 9a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 3a + a2) = 0

Factor a trinomial.
3((-6 + -1a)(3 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
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 = {-6, 3}