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

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

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

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

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

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

Combine like terms: 8b + -3b = 5b
(-6 + 5b + 4b2) = 0

Solving
-6 + 5b + 4b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-2 + -1b = 0

Solving
-2 + -1b = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1b = 0 + 2
-1b = 0 + 2

Combine like terms: 0 + 2 = 2
-1b = 2

Divide each side by '-1'.
b = -2

Simplifying
b = -2
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 = {-2, 0.75}