12a^2-a-6=0

Solution for 12a^2-a-6=0 equation:

Simplifying
12a2 + -1a + -6 = 0

Reorder the terms:
-6 + -1a + 12a2 = 0

Solving
-6 + -1a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -3a)(3 + -4a) = 0

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 '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

Solving
3 + -4a = 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 + -4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a = 0 + -3
-4a = 0 + -3

Combine like terms: 0 + -3 = -3
-4a = -3

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Solution
a = {-0.6666666667, 0.75}