30a^2-16a-24=0

Solution for 30a^2-16a-24=0 equation:

Simplifying
30a2 + -16a + -24 = 0

Reorder the terms:
-24 + -16a + 30a2 = 0

Solving
-24 + -16a + 30a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -8a + 15a2) = 0

Factor a trinomial.
2((-2 + -3a)(6 + -5a)) = 0

Ignore the factor 2.
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 '(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
Solution
a = {-0.6666666667, 1.2}