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

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

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

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

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

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

Combine like terms: 3b + -8b = -5b
(-12 + -5b + 2b2) = 0

Solving
-12 + -5b + 2b2 = 0

Solving for variable 'b'.

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

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 '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {-1.5, 4}