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Simplifying 21r3 + 51r2 + 18r = 0 Reorder the terms: 18r + 51r2 + 21r3 = 0 Solving 18r + 51r2 + 21r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r'. 3r(6 + 17r + 7r2) = 0 Factor a trinomial. 3r((2 + r)(3 + 7r)) = 0 Ignore the factor 3.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 '(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 = -2Subproblem 3
Set the factor '(3 + 7r)' equal to zero and attempt to solve: Simplifying 3 + 7r = 0 Solving 3 + 7r = 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 + 7r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7r = 0 + -3 7r = 0 + -3 Combine like terms: 0 + -3 = -3 7r = -3 Divide each side by '7'. r = -0.4285714286 Simplifying r = -0.4285714286Solution
r = {0, -2, -0.4285714286}
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