4a^10-24a^9-364a^8=0

Solution for 4a^10-24a^9-364a^8=0 equation:

Simplifying
4a10 + -24a9 + -364a8 = 0

Reorder the terms:
-364a8 + -24a9 + 4a10 = 0

Solving
-364a8 + -24a9 + 4a10 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a8'.
4a8(-91 + -6a + a2) = 0

Factor a trinomial.
4a8((-7 + -1a)(13 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a8' equal to zero and attempt to solve:

Simplifying
a8 = 0

Solving
a8 = 0

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

Simplifying
a8 = 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 '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 3
Set the factor '(13 + -1a)' equal to zero and attempt to solve:

Simplifying
13 + -1a = 0

Solving
13 + -1a = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1a = 0 + -13
-1a = 0 + -13

Combine like terms: 0 + -13 = -13
-1a = -13

Divide each side by '-1'.
a = 13

Simplifying
a = 13
Solution
a = {-7, 13}