4a^8-24a^7-288a^6=0

Solution for 4a^8-24a^7-288a^6=0 equation:

Simplifying
4a8 + -24a7 + -288a6 = 0

Reorder the terms:
-288a6 + -24a7 + 4a8 = 0

Solving
-288a6 + -24a7 + 4a8 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a6'.
4a6(-72 + -6a + a2) = 0

Factor a trinomial.
4a6((-6 + -1a)(12 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a6' equal to zero and attempt to solve:

Simplifying
a6 = 0

Solving
a6 = 0

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

Simplifying
a6 = 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 '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 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 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 3
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {-6, 12}