5a^8-5a^7-10a^6=

Solution for 5a^8-5a^7-10a^6= equation:

Simplifying
5a8 + -5a7 + -10a6 = 0

Reorder the terms:
-10a6 + -5a7 + 5a8 = 0

Solving
-10a6 + -5a7 + 5a8 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a6'.
5a6(-2 + -1a + a2) = 0

Factor a trinomial.
5a6((-1 + -1a)(2 + -1a)) = 0

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
Subproblem 3
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
Solution
a = {-1, 2}