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Simplifying 30r3 + -19r2 + -63r = 0 Reorder the terms: -63r + -19r2 + 30r3 = 0 Solving -63r + -19r2 + 30r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-63 + -19r + 30r2) = 0 Factor a trinomial. r((-7 + -6r)(9 + -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 '(-7 + -6r)' equal to zero and attempt to solve: Simplifying -7 + -6r = 0 Solving -7 + -6r = 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 + -6r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6r = 0 + 7 -6r = 0 + 7 Combine like terms: 0 + 7 = 7 -6r = 7 Divide each side by '-6'. r = -1.166666667 Simplifying r = -1.166666667Subproblem 3
Set the factor '(9 + -5r)' equal to zero and attempt to solve: Simplifying 9 + -5r = 0 Solving 9 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5r = 0 + -9 -5r = 0 + -9 Combine like terms: 0 + -9 = -9 -5r = -9 Divide each side by '-5'. r = 1.8 Simplifying r = 1.8Solution
r = {0, -1.166666667, 1.8}
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