(b+4)(2b-5)=0

Solution for (b+4)(2b-5)=0 equation:

Simplifying
(b + 4)(2b + -5) = 0

Reorder the terms:
(4 + b)(2b + -5) = 0

Reorder the terms:
(4 + b)(-5 + 2b) = 0

Multiply (4 + b) * (-5 + 2b)
(4(-5 + 2b) + b(-5 + 2b)) = 0
((-5 * 4 + 2b * 4) + b(-5 + 2b)) = 0
((-20 + 8b) + b(-5 + 2b)) = 0
(-20 + 8b + (-5 * b + 2b * b)) = 0
(-20 + 8b + (-5b + 2b2)) = 0

Combine like terms: 8b + -5b = 3b
(-20 + 3b + 2b2) = 0

Solving
-20 + 3b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-4 + -1b)(5 + -2b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -2b)' equal to zero and attempt to solve:

Simplifying
5 + -2b = 0

Solving
5 + -2b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2b = 0 + -5
-2b = 0 + -5

Combine like terms: 0 + -5 = -5
-2b = -5

Divide each side by '-2'.
b = 2.5

Simplifying
b = 2.5
Solution
b = {-4, 2.5}