(4b-3)(3b-8)=0

Solution for (4b-3)(3b-8)=0 equation:

Simplifying
(4b + -3)(3b + -8) = 0

Reorder the terms:
(-3 + 4b)(3b + -8) = 0

Reorder the terms:
(-3 + 4b)(-8 + 3b) = 0

Multiply (-3 + 4b) * (-8 + 3b)
(-3(-8 + 3b) + 4b * (-8 + 3b)) = 0
((-8 * -3 + 3b * -3) + 4b * (-8 + 3b)) = 0
((24 + -9b) + 4b * (-8 + 3b)) = 0
(24 + -9b + (-8 * 4b + 3b * 4b)) = 0
(24 + -9b + (-32b + 12b2)) = 0

Combine like terms: -9b + -32b = -41b
(24 + -41b + 12b2) = 0

Solving
24 + -41b + 12b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + -4b)(8 + -3b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -3b)' equal to zero and attempt to solve:

Simplifying
8 + -3b = 0

Solving
8 + -3b = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3b = 0 + -8
-3b = 0 + -8

Combine like terms: 0 + -8 = -8
-3b = -8

Divide each side by '-3'.
b = 2.666666667

Simplifying
b = 2.666666667
Solution
b = {0.75, 2.666666667}