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Simplifying (2r + 9)(r + 1) = 0 Reorder the terms: (9 + 2r)(r + 1) = 0 Reorder the terms: (9 + 2r)(1 + r) = 0 Multiply (9 + 2r) * (1 + r) (9(1 + r) + 2r * (1 + r)) = 0 ((1 * 9 + r * 9) + 2r * (1 + r)) = 0 ((9 + 9r) + 2r * (1 + r)) = 0 (9 + 9r + (1 * 2r + r * 2r)) = 0 (9 + 9r + (2r + 2r2)) = 0 Combine like terms: 9r + 2r = 11r (9 + 11r + 2r2) = 0 Solving 9 + 11r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (9 + 2r)(1 + r) = 0Subproblem 1
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 = -4.5Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve: Simplifying 1 + r = 0 Solving 1 + r = 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 + r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + r = 0 + -1 r = 0 + -1 Combine like terms: 0 + -1 = -1 r = -1 Simplifying r = -1Solution
r = {-4.5, -1}
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