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

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

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

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

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

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

Combine like terms: -2b + -3b = -5b
(2 + -5b + 3b2) = 0

Solving
2 + -5b + 3b2 = 0

Solving for variable 'b'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

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

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

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

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

Simplifying
b = 1
Solution
b = {0.6666666667, 1}