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Simplifying (2r + 5)(r + 2) = 0 Reorder the terms: (5 + 2r)(r + 2) = 0 Reorder the terms: (5 + 2r)(2 + r) = 0 Multiply (5 + 2r) * (2 + r) (5(2 + r) + 2r * (2 + r)) = 0 ((2 * 5 + r * 5) + 2r * (2 + r)) = 0 ((10 + 5r) + 2r * (2 + r)) = 0 (10 + 5r + (2 * 2r + r * 2r)) = 0 (10 + 5r + (4r + 2r2)) = 0 Combine like terms: 5r + 4r = 9r (10 + 9r + 2r2) = 0 Solving 10 + 9r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (5 + 2r)(2 + r) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve: Simplifying 2 + r = 0 Solving 2 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + r = 0 + -2 r = 0 + -2 Combine like terms: 0 + -2 = -2 r = -2 Simplifying r = -2Solution
r = {-2.5, -2}
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