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

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

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

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

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

Multiply (-3 + 2b) * (3 + 4b)
(-3(3 + 4b) + 2b * (3 + 4b)) = 0
((3 * -3 + 4b * -3) + 2b * (3 + 4b)) = 0
((-9 + -12b) + 2b * (3 + 4b)) = 0
(-9 + -12b + (3 * 2b + 4b * 2b)) = 0
(-9 + -12b + (6b + 8b2)) = 0

Combine like terms: -12b + 6b = -6b
(-9 + -6b + 8b2) = 0

Solving
-9 + -6b + 8b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-3 + -4b)(3 + -2b) = 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 '(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
Solution
b = {-0.75, 1.5}