(6b-3)(2-b)=0

Solution for (6b-3)(2-b)=0 equation:

Simplifying
(6b + -3)(2 + -1b) = 0

Reorder the terms:
(-3 + 6b)(2 + -1b) = 0

Multiply (-3 + 6b) * (2 + -1b)
(-3(2 + -1b) + 6b * (2 + -1b)) = 0
((2 * -3 + -1b * -3) + 6b * (2 + -1b)) = 0
((-6 + 3b) + 6b * (2 + -1b)) = 0
(-6 + 3b + (2 * 6b + -1b * 6b)) = 0
(-6 + 3b + (12b + -6b2)) = 0

Combine like terms: 3b + 12b = 15b
(-6 + 15b + -6b2) = 0

Solving
-6 + 15b + -6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 5b + -2b2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + b)' equal to zero and attempt to solve:

Simplifying
-2 + b = 0

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

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

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

Simplifying
b = 2
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
Solution
b = {2, 0.5}