2((-9+-1a)(1+-3a))=0

Solution for 2((-9+-1a)(1+-3a))=0 equation:

Simplifying
2((-9 + -1a)(1 + -3a)) = 0

Multiply (-9 + -1a) * (1 + -3a)
2((-9(1 + -3a) + -1a * (1 + -3a))) = 0
2(((1 * -9 + -3a * -9) + -1a * (1 + -3a))) = 0
2(((-9 + 27a) + -1a * (1 + -3a))) = 0
2((-9 + 27a + (1 * -1a + -3a * -1a))) = 0
2((-9 + 27a + (-1a + 3a2))) = 0

Combine like terms: 27a + -1a = 26a
2((-9 + 26a + 3a2)) = 0
(-9 * 2 + 26a * 2 + 3a2 * 2) = 0
(-18 + 52a + 6a2) = 0

Solving
-18 + 52a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 26a + 3a2) = 0

Factor a trinomial.
2((-9 + -1a)(1 + -3a)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -3a)' equal to zero and attempt to solve:

Simplifying
1 + -3a = 0

Solving
1 + -3a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3a = 0 + -1
-3a = 0 + -1

Combine like terms: 0 + -1 = -1
-3a = -1

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {-9, 0.3333333333}