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Simplifying (4r + 5)(5r + 8) = 0 Reorder the terms: (5 + 4r)(5r + 8) = 0 Reorder the terms: (5 + 4r)(8 + 5r) = 0 Multiply (5 + 4r) * (8 + 5r) (5(8 + 5r) + 4r * (8 + 5r)) = 0 ((8 * 5 + 5r * 5) + 4r * (8 + 5r)) = 0 ((40 + 25r) + 4r * (8 + 5r)) = 0 (40 + 25r + (8 * 4r + 5r * 4r)) = 0 (40 + 25r + (32r + 20r2)) = 0 Combine like terms: 25r + 32r = 57r (40 + 57r + 20r2) = 0 Solving 40 + 57r + 20r2 = 0 Solving for variable 'r'. Factor a trinomial. (8 + 5r)(5 + 4r) = 0Subproblem 1
Set the factor '(8 + 5r)' equal to zero and attempt to solve: Simplifying 8 + 5r = 0 Solving 8 + 5r = 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 + 5r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5r = 0 + -8 5r = 0 + -8 Combine like terms: 0 + -8 = -8 5r = -8 Divide each side by '5'. r = -1.6 Simplifying r = -1.6Subproblem 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 = {-1.6, -1.25}
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