(3b+4)(7b-1)=0

Solution for (3b+4)(7b-1)=0 equation:

Simplifying
(3b + 4)(7b + -1) = 0

Reorder the terms:
(4 + 3b)(7b + -1) = 0

Reorder the terms:
(4 + 3b)(-1 + 7b) = 0

Multiply (4 + 3b) * (-1 + 7b)
(4(-1 + 7b) + 3b * (-1 + 7b)) = 0
((-1 * 4 + 7b * 4) + 3b * (-1 + 7b)) = 0
((-4 + 28b) + 3b * (-1 + 7b)) = 0
(-4 + 28b + (-1 * 3b + 7b * 3b)) = 0
(-4 + 28b + (-3b + 21b2)) = 0

Combine like terms: 28b + -3b = 25b
(-4 + 25b + 21b2) = 0

Solving
-4 + 25b + 21b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-4 + -3b)(1 + -7b) = 0

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

Simplifying
-4 + -3b = 0

Solving
-4 + -3b = 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 + -3b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3b = 0 + 4
-3b = 0 + 4

Combine like terms: 0 + 4 = 4
-3b = 4

Divide each side by '-3'.
b = -1.333333333

Simplifying
b = -1.333333333
Subproblem 2
Set the factor '(1 + -7b)' equal to zero and attempt to solve:

Simplifying
1 + -7b = 0

Solving
1 + -7b = 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 + -7b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7b = 0 + -1
-7b = 0 + -1

Combine like terms: 0 + -1 = -1
-7b = -1

Divide each side by '-7'.
b = 0.1428571429

Simplifying
b = 0.1428571429
Solution
b = {-1.333333333, 0.1428571429}