30a^2+31a-6=0

Solution for 30a^2+31a-6=0 equation:

Simplifying
30a2 + 31a + -6 = 0

Reorder the terms:
-6 + 31a + 30a2 = 0

Solving
-6 + 31a + 30a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -5a)(1 + -6a) = 0

Subproblem 1
Set the factor '(-6 + -5a)' equal to zero and attempt to solve:

Simplifying
-6 + -5a = 0

Solving
-6 + -5a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5a = 0 + 6
-5a = 0 + 6

Combine like terms: 0 + 6 = 6
-5a = 6

Divide each side by '-5'.
a = -1.2

Simplifying
a = -1.2
Subproblem 2
Set the factor '(1 + -6a)' equal to zero and attempt to solve:

Simplifying
1 + -6a = 0

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

Combine like terms: 1 + -1 = 0
0 + -6a = 0 + -1
-6a = 0 + -1

Combine like terms: 0 + -1 = -1
-6a = -1

Divide each side by '-6'.
a = 0.1666666667

Simplifying
a = 0.1666666667
Solution
a = {-1.2, 0.1666666667}