12a^2-31a-15=0

Solution for 12a^2-31a-15=0 equation:

Simplifying
12a2 + -31a + -15 = 0

Reorder the terms:
-15 + -31a + 12a2 = 0

Solving
-15 + -31a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -12a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-5 + -12a)' equal to zero and attempt to solve:

Simplifying
-5 + -12a = 0

Solving
-5 + -12a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -12a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -12a = 0 + 5
-12a = 0 + 5

Combine like terms: 0 + 5 = 5
-12a = 5

Divide each side by '-12'.
a = -0.4166666667

Simplifying
a = -0.4166666667
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 = {-0.4166666667, 3}