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Simplifying 6r3 + 5r2 + 2r = 9r2 + 4r3 Reorder the terms: 2r + 5r2 + 6r3 = 9r2 + 4r3 Solving 2r + 5r2 + 6r3 = 9r2 + 4r3 Solving for variable 'r'. Reorder the terms: 2r + 5r2 + -9r2 + 6r3 + -4r3 = 9r2 + 4r3 + -9r2 + -4r3 Combine like terms: 5r2 + -9r2 = -4r2 2r + -4r2 + 6r3 + -4r3 = 9r2 + 4r3 + -9r2 + -4r3 Combine like terms: 6r3 + -4r3 = 2r3 2r + -4r2 + 2r3 = 9r2 + 4r3 + -9r2 + -4r3 Reorder the terms: 2r + -4r2 + 2r3 = 9r2 + -9r2 + 4r3 + -4r3 Combine like terms: 9r2 + -9r2 = 0 2r + -4r2 + 2r3 = 0 + 4r3 + -4r3 2r + -4r2 + 2r3 = 4r3 + -4r3 Combine like terms: 4r3 + -4r3 = 0 2r + -4r2 + 2r3 = 0 Factor out the Greatest Common Factor (GCF), '2r'. 2r(1 + -2r + r2) = 0 Factor a trinomial. 2r((1 + -1r)(1 + -1r)) = 0 Ignore the factor 2.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 '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 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 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Subproblem 3
Set the factor '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 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 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Solution
r = {0, 1, 1}
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