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

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

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

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

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

Multiply (-3 + 4b) * (1 + 2b)
(-3(1 + 2b) + 4b * (1 + 2b)) = 0
((1 * -3 + 2b * -3) + 4b * (1 + 2b)) = 0
((-3 + -6b) + 4b * (1 + 2b)) = 0
(-3 + -6b + (1 * 4b + 2b * 4b)) = 0
(-3 + -6b + (4b + 8b2)) = 0

Combine like terms: -6b + 4b = -2b
(-3 + -2b + 8b2) = 0

Solving
-3 + -2b + 8b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -2b)(3 + -4b) = 0

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 '(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 = {-0.5, 0.75}