60a^2-4a-24=0

Solution for 60a^2-4a-24=0 equation:

Simplifying
60a2 + -4a + -24 = 0

Reorder the terms:
-24 + -4a + 60a2 = 0

Solving
-24 + -4a + 60a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -1a + 15a2) = 0

Factor a trinomial.
4((-3 + -5a)(2 + -3a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -5a)' equal to zero and attempt to solve:

Simplifying
-3 + -5a = 0

Solving
-3 + -5a = 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 + -5a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5a = 0 + 3
-5a = 0 + 3

Combine like terms: 0 + 3 = 3
-5a = 3

Divide each side by '-5'.
a = -0.6

Simplifying
a = -0.6
Subproblem 2
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
Solution
a = {-0.6, 0.6666666667}