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Simplifying 6r3 + 42r2 + -180r = 0 Reorder the terms: -180r + 42r2 + 6r3 = 0 Solving -180r + 42r2 + 6r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6r'. 6r(-30 + 7r + r2) = 0 Factor a trinomial. 6r((-10 + -1r)(3 + -1r)) = 0 Ignore the factor 6.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 '(-10 + -1r)' equal to zero and attempt to solve: Simplifying -10 + -1r = 0 Solving -10 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1r = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1r = 0 + 10 -1r = 0 + 10 Combine like terms: 0 + 10 = 10 -1r = 10 Divide each side by '-1'. r = -10 Simplifying r = -10Subproblem 3
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 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 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {0, -10, 3}
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