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

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

Simplifying
a7 + 6a6b + -7a5b2 = 0

Reorder the terms:
-7a5b2 + 6a6b + a7 = 0

Solving
-7a5b2 + 6a6b + a7 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a5'.
a5(-7b2 + 6ab + a2) = 0

Factor a trinomial.
a5((-7b + -1a)(b + -1a)) = 0

Subproblem 1
Set the factor 'a5' equal to zero and attempt to solve:

Simplifying
a5 = 0

Solving
a5 = 0

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

Simplifying
a5 = 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 '(-7b + -1a)' equal to zero and attempt to solve:

Simplifying
-7b + -1a = 0

Reorder the terms:
-1a + -7b = 0

Solving
-1a + -7b = 0

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

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

Combine like terms: -7b + 7b = 0
-1a + 0 = 0 + 7b
-1a = 0 + 7b
Remove the zero:
-1a = 7b

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

Simplifying
a = -7b
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 = {-7b, b}