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Simplifying (8r + 1)(r + 5) = 0 Reorder the terms: (1 + 8r)(r + 5) = 0 Reorder the terms: (1 + 8r)(5 + r) = 0 Multiply (1 + 8r) * (5 + r) (1(5 + r) + 8r * (5 + r)) = 0 ((5 * 1 + r * 1) + 8r * (5 + r)) = 0 ((5 + 1r) + 8r * (5 + r)) = 0 (5 + 1r + (5 * 8r + r * 8r)) = 0 (5 + 1r + (40r + 8r2)) = 0 Combine like terms: 1r + 40r = 41r (5 + 41r + 8r2) = 0 Solving 5 + 41r + 8r2 = 0 Solving for variable 'r'. Factor a trinomial. (5 + r)(1 + 8r) = 0Subproblem 1
Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 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 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5Subproblem 2
Set the factor '(1 + 8r)' equal to zero and attempt to solve: Simplifying 1 + 8r = 0 Solving 1 + 8r = 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 + 8r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8r = 0 + -1 8r = 0 + -1 Combine like terms: 0 + -1 = -1 8r = -1 Divide each side by '8'. r = -0.125 Simplifying r = -0.125Solution
r = {-5, -0.125}
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