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Simplifying (4r + -5)(7r + 2) = 0 Reorder the terms: (-5 + 4r)(7r + 2) = 0 Reorder the terms: (-5 + 4r)(2 + 7r) = 0 Multiply (-5 + 4r) * (2 + 7r) (-5(2 + 7r) + 4r * (2 + 7r)) = 0 ((2 * -5 + 7r * -5) + 4r * (2 + 7r)) = 0 ((-10 + -35r) + 4r * (2 + 7r)) = 0 (-10 + -35r + (2 * 4r + 7r * 4r)) = 0 (-10 + -35r + (8r + 28r2)) = 0 Combine like terms: -35r + 8r = -27r (-10 + -27r + 28r2) = 0 Solving -10 + -27r + 28r2 = 0 Solving for variable 'r'. Factor a trinomial. (-2 + -7r)(5 + -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 '(5 + -4r)' equal to zero and attempt to solve: Simplifying 5 + -4r = 0 Solving 5 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4r = 0 + -5 -4r = 0 + -5 Combine like terms: 0 + -5 = -5 -4r = -5 Divide each side by '-4'. r = 1.25 Simplifying r = 1.25Solution
r = {-0.2857142857, 1.25}
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