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Simplifying (2r + 1)(8r + 5) = 0 Reorder the terms: (1 + 2r)(8r + 5) = 0 Reorder the terms: (1 + 2r)(5 + 8r) = 0 Multiply (1 + 2r) * (5 + 8r) (1(5 + 8r) + 2r * (5 + 8r)) = 0 ((5 * 1 + 8r * 1) + 2r * (5 + 8r)) = 0 ((5 + 8r) + 2r * (5 + 8r)) = 0 (5 + 8r + (5 * 2r + 8r * 2r)) = 0 (5 + 8r + (10r + 16r2)) = 0 Combine like terms: 8r + 10r = 18r (5 + 18r + 16r2) = 0 Solving 5 + 18r + 16r2 = 0 Solving for variable 'r'. Factor a trinomial. (5 + 8r)(1 + 2r) = 0Subproblem 1
Set the factor '(5 + 8r)' equal to zero and attempt to solve: Simplifying 5 + 8r = 0 Solving 5 + 8r = 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 + 8r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8r = 0 + -5 8r = 0 + -5 Combine like terms: 0 + -5 = -5 8r = -5 Divide each side by '8'. r = -0.625 Simplifying r = -0.625Subproblem 2
Set the factor '(1 + 2r)' equal to zero and attempt to solve: Simplifying 1 + 2r = 0 Solving 1 + 2r = 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 + 2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2r = 0 + -1 2r = 0 + -1 Combine like terms: 0 + -1 = -1 2r = -1 Divide each side by '2'. r = -0.5 Simplifying r = -0.5Solution
r = {-0.625, -0.5}
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