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Simplifying -18r + 3r2 + 15r3 = 0 Solving -18r + 3r2 + 15r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r'. 3r(-6 + r + 5r2) = 0 Factor a trinomial. 3r((-6 + -5r)(1 + -1r)) = 0 Ignore the factor 3.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 '(-6 + -5r)' equal to zero and attempt to solve: Simplifying -6 + -5r = 0 Solving -6 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5r = 0 + 6 -5r = 0 + 6 Combine like terms: 0 + 6 = 6 -5r = 6 Divide each side by '-5'. r = -1.2 Simplifying r = -1.2Subproblem 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, -1.2, 1}
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