(4b+3)(b+1)=0

Solution for (4b+3)(b+1)=0 equation:

Simplifying
(4b + 3)(b + 1) = 0

Reorder the terms:
(3 + 4b)(b + 1) = 0

Reorder the terms:
(3 + 4b)(1 + b) = 0

Multiply (3 + 4b) * (1 + b)
(3(1 + b) + 4b * (1 + b)) = 0
((1 * 3 + b * 3) + 4b * (1 + b)) = 0
((3 + 3b) + 4b * (1 + b)) = 0
(3 + 3b + (1 * 4b + b * 4b)) = 0
(3 + 3b + (4b + 4b2)) = 0

Combine like terms: 3b + 4b = 7b
(3 + 7b + 4b2) = 0

Solving
3 + 7b + 4b2 = 0

Solving for variable 'b'.

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

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

Simplifying
1 + b = 0

Solving
1 + b = 0

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

Add '-1' to each side of the equation.
1 + -1 + b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + b = 0 + -1
b = 0 + -1

Combine like terms: 0 + -1 = -1
b = -1

Simplifying
b = -1
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 = {-1, -0.75}