(-6b+9)(8b-1)=0

Solution for (-6b+9)(8b-1)=0 equation:

Simplifying
(-6b + 9)(8b + -1) = 0

Reorder the terms:
(9 + -6b)(8b + -1) = 0

Reorder the terms:
(9 + -6b)(-1 + 8b) = 0

Multiply (9 + -6b) * (-1 + 8b)
(9(-1 + 8b) + -6b * (-1 + 8b)) = 0
((-1 * 9 + 8b * 9) + -6b * (-1 + 8b)) = 0
((-9 + 72b) + -6b * (-1 + 8b)) = 0
(-9 + 72b + (-1 * -6b + 8b * -6b)) = 0
(-9 + 72b + (6b + -48b2)) = 0

Combine like terms: 72b + 6b = 78b
(-9 + 78b + -48b2) = 0

Solving
-9 + 78b + -48b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 26b + -16b2) = 0

Factor a trinomial.
3((-3 + 2b)(1 + -8b)) = 0

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

Simplifying
1 + -8b = 0

Solving
1 + -8b = 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 + -8b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8b = 0 + -1
-8b = 0 + -1

Combine like terms: 0 + -1 = -1
-8b = -1

Divide each side by '-8'.
b = 0.125

Simplifying
b = 0.125
Solution
b = {1.5, 0.125}