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Simplifying (4r + 5)(r + 8) = 0 Reorder the terms: (5 + 4r)(r + 8) = 0 Reorder the terms: (5 + 4r)(8 + r) = 0 Multiply (5 + 4r) * (8 + r) (5(8 + r) + 4r * (8 + r)) = 0 ((8 * 5 + r * 5) + 4r * (8 + r)) = 0 ((40 + 5r) + 4r * (8 + r)) = 0 (40 + 5r + (8 * 4r + r * 4r)) = 0 (40 + 5r + (32r + 4r2)) = 0 Combine like terms: 5r + 32r = 37r (40 + 37r + 4r2) = 0 Solving 40 + 37r + 4r2 = 0 Solving for variable 'r'. Factor a trinomial. (8 + r)(5 + 4r) = 0Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve: Simplifying 8 + r = 0 Solving 8 + r = 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 + r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + r = 0 + -8 r = 0 + -8 Combine like terms: 0 + -8 = -8 r = -8 Simplifying r = -8Subproblem 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 = {-8, -1.25}
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