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Simplifying (2r + 3)(7r + 7) = 0 Reorder the terms: (3 + 2r)(7r + 7) = 0 Reorder the terms: (3 + 2r)(7 + 7r) = 0 Multiply (3 + 2r) * (7 + 7r) (3(7 + 7r) + 2r * (7 + 7r)) = 0 ((7 * 3 + 7r * 3) + 2r * (7 + 7r)) = 0 ((21 + 21r) + 2r * (7 + 7r)) = 0 (21 + 21r + (7 * 2r + 7r * 2r)) = 0 (21 + 21r + (14r + 14r2)) = 0 Combine like terms: 21r + 14r = 35r (21 + 35r + 14r2) = 0 Solving 21 + 35r + 14r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '7'. 7(3 + 5r + 2r2) = 0 Factor a trinomial. 7((3 + 2r)(1 + r)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(3 + 2r)' equal to zero and attempt to solve: Simplifying 3 + 2r = 0 Solving 3 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2r = 0 + -3 2r = 0 + -3 Combine like terms: 0 + -3 = -3 2r = -3 Divide each side by '2'. r = -1.5 Simplifying r = -1.5Subproblem 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 = {-1.5, -1}
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