(5b-4)(2b+1)=0

Solution for (5b-4)(2b+1)=0 equation:

Simplifying
(5b + -4)(2b + 1) = 0

Reorder the terms:
(-4 + 5b)(2b + 1) = 0

Reorder the terms:
(-4 + 5b)(1 + 2b) = 0

Multiply (-4 + 5b) * (1 + 2b)
(-4(1 + 2b) + 5b * (1 + 2b)) = 0
((1 * -4 + 2b * -4) + 5b * (1 + 2b)) = 0
((-4 + -8b) + 5b * (1 + 2b)) = 0
(-4 + -8b + (1 * 5b + 2b * 5b)) = 0
(-4 + -8b + (5b + 10b2)) = 0

Combine like terms: -8b + 5b = -3b
(-4 + -3b + 10b2) = 0

Solving
-4 + -3b + 10b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -2b)(4 + -5b) = 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 '(4 + -5b)' equal to zero and attempt to solve:

Simplifying
4 + -5b = 0

Solving
4 + -5b = 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 + -5b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5b = 0 + -4
-5b = 0 + -4

Combine like terms: 0 + -4 = -4
-5b = -4

Divide each side by '-5'.
b = 0.8

Simplifying
b = 0.8
Solution
b = {-0.5, 0.8}