8a^2-4a-24=0

Solution for 8a^2-4a-24=0 equation:

Simplifying
8a2 + -4a + -24 = 0

Reorder the terms:
-24 + -4a + 8a2 = 0

Solving
-24 + -4a + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -1a + 2a2) = 0

Factor a trinomial.
4((-3 + -2a)(2 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve:

Simplifying
-3 + -2a = 0

Solving
-3 + -2a = 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 + -2a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2a = 0 + 3
-2a = 0 + 3

Combine like terms: 0 + 3 = 3
-2a = 3

Divide each side by '-2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-1.5, 2}