a^3-4a^2b-21ab^2=0

Solution for a^3-4a^2b-21ab^2=0 equation:

Simplifying
a3 + -4a2b + -21ab2 = 0

Reorder the terms:
-21ab2 + -4a2b + a3 = 0

Solving
-21ab2 + -4a2b + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-21b2 + -4ab + a2) = 0

Factor a trinomial.
a((-3b + -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 '(-3b + -1a)' equal to zero and attempt to solve:

Simplifying
-3b + -1a = 0

Reorder the terms:
-1a + -3b = 0

Solving
-1a + -3b = 0

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

Add '3b' to each side of the equation.
-1a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
-1a + 0 = 0 + 3b
-1a = 0 + 3b
Remove the zero:
-1a = 3b

Divide each side by '-1'.
a = -3b

Simplifying
a = -3b
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, -3b, 7b}