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Simplifying r3 + 54r = 15r2 Reorder the terms: 54r + r3 = 15r2 Solving 54r + r3 = 15r2 Solving for variable 'r'. Reorder the terms: 54r + -15r2 + r3 = 15r2 + -15r2 Combine like terms: 15r2 + -15r2 = 0 54r + -15r2 + r3 = 0 Factor out the Greatest Common Factor (GCF), 'r'. r(54 + -15r + r2) = 0 Factor a trinomial. r((6 + -1r)(9 + -1r)) = 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 '(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 = 6Subproblem 3
Set the factor '(9 + -1r)' equal to zero and attempt to solve: Simplifying 9 + -1r = 0 Solving 9 + -1r = 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 + -1r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1r = 0 + -9 -1r = 0 + -9 Combine like terms: 0 + -9 = -9 -1r = -9 Divide each side by '-1'. r = 9 Simplifying r = 9Solution
r = {0, 6, 9}
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