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Simplifying (4r + -1)(7r + 2) = 0 Reorder the terms: (-1 + 4r)(7r + 2) = 0 Reorder the terms: (-1 + 4r)(2 + 7r) = 0 Multiply (-1 + 4r) * (2 + 7r) (-1(2 + 7r) + 4r * (2 + 7r)) = 0 ((2 * -1 + 7r * -1) + 4r * (2 + 7r)) = 0 ((-2 + -7r) + 4r * (2 + 7r)) = 0 (-2 + -7r + (2 * 4r + 7r * 4r)) = 0 (-2 + -7r + (8r + 28r2)) = 0 Combine like terms: -7r + 8r = 1r (-2 + 1r + 28r2) = 0 Solving -2 + 1r + 28r2 = 0 Solving for variable 'r'. Factor a trinomial. (-2 + -7r)(1 + -4r) = 0Subproblem 1
Set the factor '(-2 + -7r)' equal to zero and attempt to solve: Simplifying -2 + -7r = 0 Solving -2 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -7r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7r = 0 + 2 -7r = 0 + 2 Combine like terms: 0 + 2 = 2 -7r = 2 Divide each side by '-7'. r = -0.2857142857 Simplifying r = -0.2857142857Subproblem 2
Set the factor '(1 + -4r)' equal to zero and attempt to solve: Simplifying 1 + -4r = 0 Solving 1 + -4r = 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 + -4r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4r = 0 + -1 -4r = 0 + -1 Combine like terms: 0 + -1 = -1 -4r = -1 Divide each side by '-4'. r = 0.25 Simplifying r = 0.25Solution
r = {-0.2857142857, 0.25}
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