3b(5b-3)(3b-1)=0

Solution for 3b(5b-3)(3b-1)=0 equation:

Simplifying
3b(5b + -3)(3b + -1) = 0

Reorder the terms:
3b(-3 + 5b)(3b + -1) = 0

Reorder the terms:
3b(-3 + 5b)(-1 + 3b) = 0

Multiply (-3 + 5b) * (-1 + 3b)
3b(-3(-1 + 3b) + 5b * (-1 + 3b)) = 0
3b((-1 * -3 + 3b * -3) + 5b * (-1 + 3b)) = 0
3b((3 + -9b) + 5b * (-1 + 3b)) = 0
3b(3 + -9b + (-1 * 5b + 3b * 5b)) = 0
3b(3 + -9b + (-5b + 15b2)) = 0

Combine like terms: -9b + -5b = -14b
3b(3 + -14b + 15b2) = 0
(3 * 3b + -14b * 3b + 15b2 * 3b) = 0
(9b + -42b2 + 45b3) = 0

Solving
9b + -42b2 + 45b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3b'.
3b(3 + -14b + 15b2) = 0

Factor a trinomial.
3b((1 + -3b)(3 + -5b)) = 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 '(1 + -3b)' equal to zero and attempt to solve:

Simplifying
1 + -3b = 0

Solving
1 + -3b = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -3b = 0 + -1
-3b = 0 + -1

Combine like terms: 0 + -1 = -1
-3b = -1

Divide each side by '-3'.
b = 0.3333333333

Simplifying
b = 0.3333333333
Subproblem 3
Set the factor '(3 + -5b)' equal to zero and attempt to solve:

Simplifying
3 + -5b = 0

Solving
3 + -5b = 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 + -5b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5b = 0 + -3
-5b = 0 + -3

Combine like terms: 0 + -3 = -3
-5b = -3

Divide each side by '-5'.
b = 0.6

Simplifying
b = 0.6
Solution
b = {0, 0.3333333333, 0.6}