(2r-14)(14r-2)=0

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Solution for (2r-14)(14r-2)=0 equation:


Simplifying
(2r + -14)(14r + -2) = 0

Reorder the terms:
(-14 + 2r)(14r + -2) = 0

Reorder the terms:
(-14 + 2r)(-2 + 14r) = 0

Multiply (-14 + 2r) * (-2 + 14r)
(-14(-2 + 14r) + 2r * (-2 + 14r)) = 0
((-2 * -14 + 14r * -14) + 2r * (-2 + 14r)) = 0
((28 + -196r) + 2r * (-2 + 14r)) = 0
(28 + -196r + (-2 * 2r + 14r * 2r)) = 0
(28 + -196r + (-4r + 28r2)) = 0

Combine like terms: -196r + -4r = -200r
(28 + -200r + 28r2) = 0

Solving
28 + -200r + 28r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -50r + 7r2) = 0

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

Ignore the factor 4.

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}

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