3a^6-6a^5-24a^4=0

Solution for 3a^6-6a^5-24a^4=0 equation:

Simplifying
3a6 + -6a5 + -24a4 = 0

Reorder the terms:
-24a4 + -6a5 + 3a6 = 0

Solving
-24a4 + -6a5 + 3a6 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a4'.
3a4(-8 + -2a + a2) = 0

Factor a trinomial.
3a4((-2 + -1a)(4 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'a4' equal to zero and attempt to solve:

Simplifying
a4 = 0

Solving
a4 = 0

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

Simplifying
a4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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
Subproblem 3
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-2, 4}