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

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

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

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

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

Multiply (3 + 7b) * (-3 + 4b)
(3(-3 + 4b) + 7b * (-3 + 4b)) = 0
((-3 * 3 + 4b * 3) + 7b * (-3 + 4b)) = 0
((-9 + 12b) + 7b * (-3 + 4b)) = 0
(-9 + 12b + (-3 * 7b + 4b * 7b)) = 0
(-9 + 12b + (-21b + 28b2)) = 0

Combine like terms: 12b + -21b = -9b
(-9 + -9b + 28b2) = 0

Solving
-9 + -9b + 28b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-3 + -7b)(3 + -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 '(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 = {-0.4285714286, 0.75}