2b(3b-2)(2b-1)=0

Solution for 2b(3b-2)(2b-1)=0 equation:

Simplifying
2b(3b + -2)(2b + -1) = 0

Reorder the terms:
2b(-2 + 3b)(2b + -1) = 0

Reorder the terms:
2b(-2 + 3b)(-1 + 2b) = 0

Multiply (-2 + 3b) * (-1 + 2b)
2b(-2(-1 + 2b) + 3b * (-1 + 2b)) = 0
2b((-1 * -2 + 2b * -2) + 3b * (-1 + 2b)) = 0
2b((2 + -4b) + 3b * (-1 + 2b)) = 0
2b(2 + -4b + (-1 * 3b + 2b * 3b)) = 0
2b(2 + -4b + (-3b + 6b2)) = 0

Combine like terms: -4b + -3b = -7b
2b(2 + -7b + 6b2) = 0
(2 * 2b + -7b * 2b + 6b2 * 2b) = 0
(4b + -14b2 + 12b3) = 0

Solving
4b + -14b2 + 12b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2b'.
2b(2 + -7b + 6b2) = 0

Factor a trinomial.
2b((1 + -2b)(2 + -3b)) = 0

Ignore the factor 2.
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 + -2b)' equal to zero and attempt to solve:

Simplifying
1 + -2b = 0

Solving
1 + -2b = 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 + -2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2b = 0 + -1
-2b = 0 + -1

Combine like terms: 0 + -1 = -1
-2b = -1

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
Subproblem 3
Set the factor '(2 + -3b)' equal to zero and attempt to solve:

Simplifying
2 + -3b = 0

Solving
2 + -3b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3b = 0 + -2
-3b = 0 + -2

Combine like terms: 0 + -2 = -2
-3b = -2

Divide each side by '-3'.
b = 0.6666666667

Simplifying
b = 0.6666666667
Solution
b = {0, 0.5, 0.6666666667}