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Simplifying 15r2 + -108r + 15 = -6r2 Reorder the terms: 15 + -108r + 15r2 = -6r2 Solving 15 + -108r + 15r2 = -6r2 Solving for variable 'r'. Combine like terms: 15r2 + 6r2 = 21r2 15 + -108r + 21r2 = -6r2 + 6r2 Combine like terms: -6r2 + 6r2 = 0 15 + -108r + 21r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -36r + 7r2) = 0 Factor a trinomial. 3((1 + -7r)(5 + -1r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -7r)' equal to zero and attempt to solve: Simplifying 1 + -7r = 0 Solving 1 + -7r = 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 + -7r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7r = 0 + -1 -7r = 0 + -1 Combine like terms: 0 + -1 = -1 -7r = -1 Divide each side by '-7'. r = 0.1428571429 Simplifying r = 0.1428571429Subproblem 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 = 5Solution
r = {0.1428571429, 5}
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