(7b+3)(9b+4)=0

Solution for (7b+3)(9b+4)=0 equation:

Simplifying
(7b + 3)(9b + 4) = 0

Reorder the terms:
(3 + 7b)(9b + 4) = 0

Reorder the terms:
(3 + 7b)(4 + 9b) = 0

Multiply (3 + 7b) * (4 + 9b)
(3(4 + 9b) + 7b * (4 + 9b)) = 0
((4 * 3 + 9b * 3) + 7b * (4 + 9b)) = 0
((12 + 27b) + 7b * (4 + 9b)) = 0
(12 + 27b + (4 * 7b + 9b * 7b)) = 0
(12 + 27b + (28b + 63b2)) = 0

Combine like terms: 27b + 28b = 55b
(12 + 55b + 63b2) = 0

Solving
12 + 55b + 63b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(4 + 9b)(3 + 7b) = 0

Subproblem 1
Set the factor '(4 + 9b)' equal to zero and attempt to solve:

Simplifying
4 + 9b = 0

Solving
4 + 9b = 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 + 9b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9b = 0 + -4
9b = 0 + -4

Combine like terms: 0 + -4 = -4
9b = -4

Divide each side by '9'.
b = -0.4444444444

Simplifying
b = -0.4444444444
Subproblem 2
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
Solution
b = {-0.4444444444, -0.4285714286}