(4b-3)(5b+4)=0

Solution for (4b-3)(5b+4)=0 equation:

Simplifying
(4b + -3)(5b + 4) = 0

Reorder the terms:
(-3 + 4b)(5b + 4) = 0

Reorder the terms:
(-3 + 4b)(4 + 5b) = 0

Multiply (-3 + 4b) * (4 + 5b)
(-3(4 + 5b) + 4b * (4 + 5b)) = 0
((4 * -3 + 5b * -3) + 4b * (4 + 5b)) = 0
((-12 + -15b) + 4b * (4 + 5b)) = 0
(-12 + -15b + (4 * 4b + 5b * 4b)) = 0
(-12 + -15b + (16b + 20b2)) = 0

Combine like terms: -15b + 16b = 1b
(-12 + 1b + 20b2) = 0

Solving
-12 + 1b + 20b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-4 + -5b)(3 + -4b) = 0

Subproblem 1
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
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 = {-0.8, 0.75}