(6b-42)(42b-6)=0

Solution for (6b-42)(42b-6)=0 equation:

Simplifying
(6b + -42)(42b + -6) = 0

Reorder the terms:
(-42 + 6b)(42b + -6) = 0

Reorder the terms:
(-42 + 6b)(-6 + 42b) = 0

Multiply (-42 + 6b) * (-6 + 42b)
(-42(-6 + 42b) + 6b * (-6 + 42b)) = 0
((-6 * -42 + 42b * -42) + 6b * (-6 + 42b)) = 0
((252 + -1764b) + 6b * (-6 + 42b)) = 0
(252 + -1764b + (-6 * 6b + 42b * 6b)) = 0
(252 + -1764b + (-36b + 252b2)) = 0

Combine like terms: -1764b + -36b = -1800b
(252 + -1800b + 252b2) = 0

Solving
252 + -1800b + 252b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '36'.
36(7 + -50b + 7b2) = 0

Factor a trinomial.
36((1 + -7b)(7 + -1b)) = 0

Ignore the factor 36.
Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

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

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

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

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {0.1428571429, 7}