(6r-42)(42r-6)=0

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

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

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

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

Multiply (-42 + 6r) * (-6 + 42r)
(-42(-6 + 42r) + 6r * (-6 + 42r)) = 0
((-6 * -42 + 42r * -42) + 6r * (-6 + 42r)) = 0
((252 + -1764r) + 6r * (-6 + 42r)) = 0
(252 + -1764r + (-6 * 6r + 42r * 6r)) = 0
(252 + -1764r + (-36r + 252r2)) = 0

Combine like terms: -1764r + -36r = -1800r
(252 + -1800r + 252r2) = 0

Solving
252 + -1800r + 252r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '36'.
36(7 + -50r + 7r2) = 0

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

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

Simplifying
1 + -7r = 0

Solving
1 + -7r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7r = 0 + -1

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

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

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

Simplifying
r = 0.1428571429
Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

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

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

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

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