(3b-2)(8b-6)=0

Solution for (3b-2)(8b-6)=0 equation:

Simplifying
(3b + -2)(8b + -6) = 0

Reorder the terms:
(-2 + 3b)(8b + -6) = 0

Reorder the terms:
(-2 + 3b)(-6 + 8b) = 0

Multiply (-2 + 3b) * (-6 + 8b)
(-2(-6 + 8b) + 3b * (-6 + 8b)) = 0
((-6 * -2 + 8b * -2) + 3b * (-6 + 8b)) = 0
((12 + -16b) + 3b * (-6 + 8b)) = 0
(12 + -16b + (-6 * 3b + 8b * 3b)) = 0
(12 + -16b + (-18b + 24b2)) = 0

Combine like terms: -16b + -18b = -34b
(12 + -34b + 24b2) = 0

Solving
12 + -34b + 24b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -17b + 12b2) = 0

Factor a trinomial.
2((2 + -3b)(3 + -4b)) = 0

Ignore the factor 2.
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 + -4b)' equal to zero and attempt to solve:

Simplifying
3 + -4b = 0

Solving
3 + -4b = 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 + -4b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4b = 0 + -3
-4b = 0 + -3

Combine like terms: 0 + -3 = -3
-4b = -3

Divide each side by '-4'.
b = 0.75

Simplifying
b = 0.75
Solution
b = {0.6666666667, 0.75}