a^6+7a^5b-8a^4b^2=0

Solution for a^6+7a^5b-8a^4b^2=0 equation:

Simplifying
a6 + 7a5b + -8a4b2 = 0

Reorder the terms:
-8a4b2 + 7a5b + a6 = 0

Solving
-8a4b2 + 7a5b + a6 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a4'.
a4(-8b2 + 7ab + a2) = 0

Factor a trinomial.
a4((-8b + -1a)(b + -1a)) = 0

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 '(-8b + -1a)' equal to zero and attempt to solve:

Simplifying
-8b + -1a = 0

Reorder the terms:
-1a + -8b = 0

Solving
-1a + -8b = 0

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

Add '8b' to each side of the equation.
-1a + -8b + 8b = 0 + 8b

Combine like terms: -8b + 8b = 0
-1a + 0 = 0 + 8b
-1a = 0 + 8b
Remove the zero:
-1a = 8b

Divide each side by '-1'.
a = -8b

Simplifying
a = -8b
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 = {-8b, b}