(6r-48)(48r-6)=0

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Solution for (6r-48)(48r-6)=0 equation: 


Simplifying
(6r + -48)(48r + -6) = 0

Reorder the terms:
(-48 + 6r)(48r + -6) = 0

Reorder the terms:
(-48 + 6r)(-6 + 48r) = 0

Multiply (-48 + 6r) * (-6 + 48r)
(-48(-6 + 48r) + 6r * (-6 + 48r)) = 0
((-6 * -48 + 48r * -48) + 6r * (-6 + 48r)) = 0
((288 + -2304r) + 6r * (-6 + 48r)) = 0
(288 + -2304r + (-6 * 6r + 48r * 6r)) = 0
(288 + -2304r + (-36r + 288r2)) = 0

Combine like terms: -2304r + -36r = -2340r
(288 + -2340r + 288r2) = 0

Solving
288 + -2340r + 288r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '36'.
36(8 + -65r + 8r2) = 0

Factor a trinomial.
36((1 + -8r)(8 + -1r)) = 0

Ignore the factor 36.

Subproblem 1
Set the factor '(1 + -8r)' equal to zero and attempt to solve:

Simplifying
1 + -8r = 0

Solving
1 + -8r = 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 + -8r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8r = 0 + -1
-8r = 0 + -1

Combine like terms: 0 + -1 = -1
-8r = -1

Divide each side by '-8'.
r = 0.125

Simplifying
r = 0.125

Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {0.125, 8}

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