9a^2-3a-6=0

Solution for 9a^2-3a-6=0 equation:

Simplifying
9a2 + -3a + -6 = 0

Reorder the terms:
-6 + -3a + 9a2 = 0

Solving
-6 + -3a + 9a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1a + 3a2) = 0

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

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

Simplifying
-2 + -3a = 0

Solving
-2 + -3a = 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 + -3a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3a = 0 + 2
-3a = 0 + 2

Combine like terms: 0 + 2 = 2
-3a = 2

Divide each side by '-3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Solution
a = {-0.6666666667, 1}