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Simplifying 8r3 + 84r2 + 196r = 0 Reorder the terms: 196r + 84r2 + 8r3 = 0 Solving 196r + 84r2 + 8r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4r'. 4r(49 + 21r + 2r2) = 0 Factor a trinomial. 4r((7 + r)(7 + 2r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
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 3
Set the factor '(7 + 2r)' equal to zero and attempt to solve: Simplifying 7 + 2r = 0 Solving 7 + 2r = 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 + 2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2r = 0 + -7 2r = 0 + -7 Combine like terms: 0 + -7 = -7 2r = -7 Divide each side by '2'. r = -3.5 Simplifying r = -3.5Solution
r = {0, -7, -3.5}
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