24a^2-56a-320=0

Solution for 24a^2-56a-320=0 equation:

Simplifying
24a2 + -56a + -320 = 0

Reorder the terms:
-320 + -56a + 24a2 = 0

Solving
-320 + -56a + 24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-40 + -7a + 3a2) = 0

Factor a trinomial.
8((-8 + -3a)(5 + -1a)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-8 + -3a)' equal to zero and attempt to solve:

Simplifying
-8 + -3a = 0

Solving
-8 + -3a = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3a = 0 + 8
-3a = 0 + 8

Combine like terms: 0 + 8 = 8
-3a = 8

Divide each side by '-3'.
a = -2.666666667

Simplifying
a = -2.666666667
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-2.666666667, 5}