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Simplifying r4 + -11r3 + 30r2 = 0 Reorder the terms: 30r2 + -11r3 + r4 = 0 Solving 30r2 + -11r3 + r4 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r2'. r2(30 + -11r + r2) = 0 Factor a trinomial. r2((5 + -1r)(6 + -1r)) = 0Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 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 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5Subproblem 3
Set the factor '(6 + -1r)' equal to zero and attempt to solve: Simplifying 6 + -1r = 0 Solving 6 + -1r = 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 + -1r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1r = 0 + -6 -1r = 0 + -6 Combine like terms: 0 + -6 = -6 -1r = -6 Divide each side by '-1'. r = 6 Simplifying r = 6Solution
r = {0, 5, 6}
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