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

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

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

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

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

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

Combine like terms: 12b + 7b = 19b
(28 + 19b + 3b2) = 0

Solving
28 + 19b + 3b2 = 0

Solving for variable 'b'.

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

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

Simplifying
4 + b = 0

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

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

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

Simplifying
b = -4
Subproblem 2
Set the factor '(7 + 3b)' equal to zero and attempt to solve:

Simplifying
7 + 3b = 0

Solving
7 + 3b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 3b = 0 + -7

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

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

Divide each side by '3'.
b = -2.333333333

Simplifying
b = -2.333333333
Solution
b = {-4, -2.333333333}