a^3+3a^2b-28ab^2=0

Solution for a^3+3a^2b-28ab^2=0 equation:

Simplifying
a3 + 3a2b + -28ab2 = 0

Reorder the terms:
-28ab2 + 3a2b + a3 = 0

Solving
-28ab2 + 3a2b + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-28b2 + 3ab + a2) = 0

Factor a trinomial.
a((-7b + -1a)(4b + -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 '(-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 '(4b + -1a)' equal to zero and attempt to solve:

Simplifying
4b + -1a = 0

Reorder the terms:
-1a + 4b = 0

Solving
-1a + 4b = 0

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

Add '-4b' to each side of the equation.
-1a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
-1a + 0 = 0 + -4b
-1a = 0 + -4b
Remove the zero:
-1a = -4b

Divide each side by '-1'.
a = 4b

Simplifying
a = 4b
Solution
a = {0, -7b, 4b}