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Simplifying 20r3 + 9r2 + r = 0 Reorder the terms: r + 9r2 + 20r3 = 0 Solving r + 9r2 + 20r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(1 + 9r + 20r2) = 0 Factor a trinomial. r((1 + 4r)(1 + 5r)) = 0Subproblem 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 '(1 + 4r)' equal to zero and attempt to solve: Simplifying 1 + 4r = 0 Solving 1 + 4r = 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 + 4r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4r = 0 + -1 4r = 0 + -1 Combine like terms: 0 + -1 = -1 4r = -1 Divide each side by '4'. r = -0.25 Simplifying r = -0.25Subproblem 3
Set the factor '(1 + 5r)' equal to zero and attempt to solve: Simplifying 1 + 5r = 0 Solving 1 + 5r = 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 + 5r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5r = 0 + -1 5r = 0 + -1 Combine like terms: 0 + -1 = -1 5r = -1 Divide each side by '5'. r = -0.2 Simplifying r = -0.2Solution
r = {0, -0.25, -0.2}
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