(-4b+2)(3b-1)=0

Solution for (-4b+2)(3b-1)=0 equation:

Simplifying
(-4b + 2)(3b + -1) = 0

Reorder the terms:
(2 + -4b)(3b + -1) = 0

Reorder the terms:
(2 + -4b)(-1 + 3b) = 0

Multiply (2 + -4b) * (-1 + 3b)
(2(-1 + 3b) + -4b * (-1 + 3b)) = 0
((-1 * 2 + 3b * 2) + -4b * (-1 + 3b)) = 0
((-2 + 6b) + -4b * (-1 + 3b)) = 0
(-2 + 6b + (-1 * -4b + 3b * -4b)) = 0
(-2 + 6b + (4b + -12b2)) = 0

Combine like terms: 6b + 4b = 10b
(-2 + 10b + -12b2) = 0

Solving
-2 + 10b + -12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 5b + -6b2) = 0

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

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

Simplifying
1 + -3b = 0

Solving
1 + -3b = 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 + -3b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3b = 0 + -1
-3b = 0 + -1

Combine like terms: 0 + -1 = -1
-3b = -1

Divide each side by '-3'.
b = 0.3333333333

Simplifying
b = 0.3333333333
Solution
b = {0.5, 0.3333333333}