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Simplifying 6r3 + 30r2 = 84r Reorder the terms: 30r2 + 6r3 = 84r Solving 30r2 + 6r3 = 84r Solving for variable 'r'. Reorder the terms: -84r + 30r2 + 6r3 = 84r + -84r Combine like terms: 84r + -84r = 0 -84r + 30r2 + 6r3 = 0 Factor out the Greatest Common Factor (GCF), '6r'. 6r(-14 + 5r + r2) = 0 Factor a trinomial. 6r((-7 + -1r)(2 + -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 '(-7 + -1r)' equal to zero and attempt to solve: Simplifying -7 + -1r = 0 Solving -7 + -1r = 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 + -1r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1r = 0 + 7 -1r = 0 + 7 Combine like terms: 0 + 7 = 7 -1r = 7 Divide each side by '-1'. r = -7 Simplifying r = -7Subproblem 3
Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 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 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2Solution
r = {0, -7, 2}
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