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Simplifying 30r5 + 63r4 + -30r3 = 0 Reorder the terms: -30r3 + 63r4 + 30r5 = 0 Solving -30r3 + 63r4 + 30r5 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r3'. 3r3(-10 + 21r + 10r2) = 0 Factor a trinomial. 3r3((-5 + -2r)(2 + -5r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve: Simplifying r3 = 0 Solving r3 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5 + -2r)' equal to zero and attempt to solve: Simplifying -5 + -2r = 0 Solving -5 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2r = 0 + 5 -2r = 0 + 5 Combine like terms: 0 + 5 = 5 -2r = 5 Divide each side by '-2'. r = -2.5 Simplifying r = -2.5Subproblem 3
Set the factor '(2 + -5r)' equal to zero and attempt to solve: Simplifying 2 + -5r = 0 Solving 2 + -5r = 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 + -5r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5r = 0 + -2 -5r = 0 + -2 Combine like terms: 0 + -2 = -2 -5r = -2 Divide each side by '-5'. r = 0.4 Simplifying r = 0.4Solution
r = {-2.5, 0.4}
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