(7b+3)(4b-5)=0

Solution for (7b+3)(4b-5)=0 equation:

Simplifying
(7b + 3)(4b + -5) = 0

Reorder the terms:
(3 + 7b)(4b + -5) = 0

Reorder the terms:
(3 + 7b)(-5 + 4b) = 0

Multiply (3 + 7b) * (-5 + 4b)
(3(-5 + 4b) + 7b * (-5 + 4b)) = 0
((-5 * 3 + 4b * 3) + 7b * (-5 + 4b)) = 0
((-15 + 12b) + 7b * (-5 + 4b)) = 0
(-15 + 12b + (-5 * 7b + 4b * 7b)) = 0
(-15 + 12b + (-35b + 28b2)) = 0

Combine like terms: 12b + -35b = -23b
(-15 + -23b + 28b2) = 0

Solving
-15 + -23b + 28b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-3 + -7b)(5 + -4b) = 0

Subproblem 1
Set the factor '(-3 + -7b)' equal to zero and attempt to solve:

Simplifying
-3 + -7b = 0

Solving
-3 + -7b = 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 + -7b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7b = 0 + 3
-7b = 0 + 3

Combine like terms: 0 + 3 = 3
-7b = 3

Divide each side by '-7'.
b = -0.4285714286

Simplifying
b = -0.4285714286
Subproblem 2
Set the factor '(5 + -4b)' equal to zero and attempt to solve:

Simplifying
5 + -4b = 0

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

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

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

Divide each side by '-4'.
b = 1.25

Simplifying
b = 1.25
Solution
b = {-0.4285714286, 1.25}