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

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

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

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

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

Multiply (-2 + 3b) * (-3 + 2b)
(-2(-3 + 2b) + 3b * (-3 + 2b)) = 0
((-3 * -2 + 2b * -2) + 3b * (-3 + 2b)) = 0
((6 + -4b) + 3b * (-3 + 2b)) = 0
(6 + -4b + (-3 * 3b + 2b * 3b)) = 0
(6 + -4b + (-9b + 6b2)) = 0

Combine like terms: -4b + -9b = -13b
(6 + -13b + 6b2) = 0

Solving
6 + -13b + 6b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(2 + -3b)(3 + -2b) = 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 '(3 + -2b)' equal to zero and attempt to solve:

Simplifying
3 + -2b = 0

Solving
3 + -2b = 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 + -2b = 0 + -3

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

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

Divide each side by '-2'.
b = 1.5

Simplifying
b = 1.5
Solution
b = {0.6666666667, 1.5}