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

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

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

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

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

Multiply (-1 + 3b) * (4 + b)
(-1(4 + b) + 3b * (4 + b)) = 0
((4 * -1 + b * -1) + 3b * (4 + b)) = 0
((-4 + -1b) + 3b * (4 + b)) = 0
(-4 + -1b + (4 * 3b + b * 3b)) = 0
(-4 + -1b + (12b + 3b2)) = 0

Combine like terms: -1b + 12b = 11b
(-4 + 11b + 3b2) = 0

Solving
-4 + 11b + 3b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-4 + -1b = 0

Solving
-4 + -1b = 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 + -1b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1b = 0 + 4
-1b = 0 + 4

Combine like terms: 0 + 4 = 4
-1b = 4

Divide each side by '-1'.
b = -4

Simplifying
b = -4
Subproblem 2
Set the factor '(1 + -3b)' equal to zero and attempt to solve:

Simplifying
1 + -3b = 0

Solving
1 + -3b = 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 + -3b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3b = 0 + -1
-3b = 0 + -1

Combine like terms: 0 + -1 = -1
-3b = -1

Divide each side by '-3'.
b = 0.3333333333

Simplifying
b = 0.3333333333
Solution
b = {-4, 0.3333333333}