(7r-1)(r-3)=0

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Solution for (7r-1)(r-3)=0 equation:


Simplifying
(7r + -1)(r + -3) = 0

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

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

Multiply (-1 + 7r) * (-3 + r)
(-1(-3 + r) + 7r * (-3 + r)) = 0
((-3 * -1 + r * -1) + 7r * (-3 + r)) = 0
((3 + -1r) + 7r * (-3 + r)) = 0
(3 + -1r + (-3 * 7r + r * 7r)) = 0
(3 + -1r + (-21r + 7r2)) = 0

Combine like terms: -1r + -21r = -22r
(3 + -22r + 7r2) = 0

Solving
3 + -22r + 7r2 = 0

Solving for variable 'r'.

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

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 '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3

Solution

r = {0.1428571429, 3}

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