30a^2-3a-6=

Solution for 30a^2-3a-6= equation:

Simplifying
30a2 + -3a + -6 = 0

Reorder the terms:
-6 + -3a + 30a2 = 0

Solving
-6 + -3a + 30a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1a + 10a2) = 0

Factor a trinomial.
3((-2 + -5a)(1 + -2a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -5a)' equal to zero and attempt to solve:

Simplifying
-2 + -5a = 0

Solving
-2 + -5a = 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 + -5a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5a = 0 + 2
-5a = 0 + 2

Combine like terms: 0 + 2 = 2
-5a = 2

Divide each side by '-5'.
a = -0.4

Simplifying
a = -0.4
Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve:

Simplifying
1 + -2a = 0

Solving
1 + -2a = 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 + -2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a = 0 + -1
-2a = 0 + -1

Combine like terms: 0 + -1 = -1
-2a = -1

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Solution
a = {-0.4, 0.5}