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Simplifying (2r + 9)(r + 5) = 0 Reorder the terms: (9 + 2r)(r + 5) = 0 Reorder the terms: (9 + 2r)(5 + r) = 0 Multiply (9 + 2r) * (5 + r) (9(5 + r) + 2r * (5 + r)) = 0 ((5 * 9 + r * 9) + 2r * (5 + r)) = 0 ((45 + 9r) + 2r * (5 + r)) = 0 (45 + 9r + (5 * 2r + r * 2r)) = 0 (45 + 9r + (10r + 2r2)) = 0 Combine like terms: 9r + 10r = 19r (45 + 19r + 2r2) = 0 Solving 45 + 19r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (5 + r)(9 + 2r) = 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 '(9 + 2r)' equal to zero and attempt to solve: Simplifying 9 + 2r = 0 Solving 9 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2r = 0 + -9 2r = 0 + -9 Combine like terms: 0 + -9 = -9 2r = -9 Divide each side by '2'. r = -4.5 Simplifying r = -4.5Solution
r = {-5, -4.5}
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