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Simplifying (r + 5)(r + 3) = 8 Reorder the terms: (5 + r)(r + 3) = 8 Reorder the terms: (5 + r)(3 + r) = 8 Multiply (5 + r) * (3 + r) (5(3 + r) + r(3 + r)) = 8 ((3 * 5 + r * 5) + r(3 + r)) = 8 ((15 + 5r) + r(3 + r)) = 8 (15 + 5r + (3 * r + r * r)) = 8 (15 + 5r + (3r + r2)) = 8 Combine like terms: 5r + 3r = 8r (15 + 8r + r2) = 8 Solving 15 + 8r + r2 = 8 Solving for variable 'r'. Reorder the terms: 15 + -8 + 8r + r2 = 8 + -8 Combine like terms: 15 + -8 = 7 7 + 8r + r2 = 8 + -8 Combine like terms: 8 + -8 = 0 7 + 8r + r2 = 0 Factor a trinomial. (7 + r)(1 + r) = 0Subproblem 1
Set the factor '(7 + r)' equal to zero and attempt to solve: Simplifying 7 + r = 0 Solving 7 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + r = 0 + -7 r = 0 + -7 Combine like terms: 0 + -7 = -7 r = -7 Simplifying r = -7Subproblem 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 = {-7, -1}
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