a^9+8a^8b-9a^7b^2=0

Solution for a^9+8a^8b-9a^7b^2=0 equation:

Simplifying
a9 + 8a8b + -9a7b2 = 0

Reorder the terms:
-9a7b2 + 8a8b + a9 = 0

Solving
-9a7b2 + 8a8b + a9 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a7'.
a7(-9b2 + 8ab + a2) = 0

Factor a trinomial.
a7((-9b + -1a)(b + -1a)) = 0

Subproblem 1
Set the factor 'a7' equal to zero and attempt to solve:

Simplifying
a7 = 0

Solving
a7 = 0

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

Simplifying
a7 = 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 '(-9b + -1a)' equal to zero and attempt to solve:

Simplifying
-9b + -1a = 0

Reorder the terms:
-1a + -9b = 0

Solving
-1a + -9b = 0

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

Add '9b' to each side of the equation.
-1a + -9b + 9b = 0 + 9b

Combine like terms: -9b + 9b = 0
-1a + 0 = 0 + 9b
-1a = 0 + 9b
Remove the zero:
-1a = 9b

Divide each side by '-1'.
a = -9b

Simplifying
a = -9b
Subproblem 3
Set the factor '(b + -1a)' equal to zero and attempt to solve:

Simplifying
b + -1a = 0

Reorder the terms:
-1a + b = 0

Solving
-1a + b = 0

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

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

Combine like terms: b + -1b = 0
-1a + 0 = 0 + -1b
-1a = 0 + -1b
Remove the zero:
-1a = -1b

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

Simplifying
a = b
Solution
a = {-9b, b}