3b^3-27b=0

Solution for 3b^3-27b=0 equation:

Simplifying
3b3 + -27b = 0

Reorder the terms:
-27b + 3b3 = 0

Solving
-27b + 3b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3b'.
3b(-9 + b2) = 0

Factor a difference between two squares.
3b((3 + b)(-3 + b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

Solving
3 + b = 0

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

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

Combine like terms: 3 + -3 = 0
0 + b = 0 + -3
b = 0 + -3

Combine like terms: 0 + -3 = -3
b = -3

Simplifying
b = -3
Subproblem 3
Set the factor '(-3 + b)' equal to zero and attempt to solve:

Simplifying
-3 + b = 0

Solving
-3 + b = 0

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

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

Combine like terms: -3 + 3 = 0
0 + b = 0 + 3
b = 0 + 3

Combine like terms: 0 + 3 = 3
b = 3

Simplifying
b = 3
Solution
b = {0, -3, 3}