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Simplifying (r + 3)(2r + 9) = 2 Reorder the terms: (3 + r)(2r + 9) = 2 Reorder the terms: (3 + r)(9 + 2r) = 2 Multiply (3 + r) * (9 + 2r) (3(9 + 2r) + r(9 + 2r)) = 2 ((9 * 3 + 2r * 3) + r(9 + 2r)) = 2 ((27 + 6r) + r(9 + 2r)) = 2 (27 + 6r + (9 * r + 2r * r)) = 2 (27 + 6r + (9r + 2r2)) = 2 Combine like terms: 6r + 9r = 15r (27 + 15r + 2r2) = 2 Solving 27 + 15r + 2r2 = 2 Solving for variable 'r'. Reorder the terms: 27 + -2 + 15r + 2r2 = 2 + -2 Combine like terms: 27 + -2 = 25 25 + 15r + 2r2 = 2 + -2 Combine like terms: 2 + -2 = 0 25 + 15r + 2r2 = 0 Factor a trinomial. (5 + r)(5 + 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 '(5 + 2r)' equal to zero and attempt to solve: Simplifying 5 + 2r = 0 Solving 5 + 2r = 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 + 2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2r = 0 + -5 2r = 0 + -5 Combine like terms: 0 + -5 = -5 2r = -5 Divide each side by '2'. r = -2.5 Simplifying r = -2.5Solution
r = {-5, -2.5}
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