a^3+7a^2b=0

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

Simplifying
a3 + 7a2b = 0

Reorder the terms:
7a2b + a3 = 0

Solving
7a2b + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(7b + a) = 0

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(7b + a)' equal to zero and attempt to solve:

Simplifying
7b + a = 0

Reorder the terms:
a + 7b = 0

Solving
a + 7b = 0

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

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

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

Simplifying
a = -7b
Solution
a = {0, -7b}