11a^2-31a-6=0

Solution for 11a^2-31a-6=0 equation:

Simplifying
11a2 + -31a + -6 = 0

Reorder the terms:
-6 + -31a + 11a2 = 0

Solving
-6 + -31a + 11a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -11a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-2 + -11a)' equal to zero and attempt to solve:

Simplifying
-2 + -11a = 0

Solving
-2 + -11a = 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 + -11a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -11a = 0 + 2
-11a = 0 + 2

Combine like terms: 0 + 2 = 2
-11a = 2

Divide each side by '-11'.
a = -0.1818181818

Simplifying
a = -0.1818181818
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 = {-0.1818181818, 3}