-8a^2b+a^3+7ab^2=0

Solution for -8a^2b+a^3+7ab^2=0 equation:

Simplifying
-8a2b + a3 + 7ab2 = 0

Reorder the terms:
7ab2 + -8a2b + a3 = 0

Solving
7ab2 + -8a2b + a3 = 0

Solving for variable 'a'.

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

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

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
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
Subproblem 3
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
Solution
a = {0, b, 7b}