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Simplifying 12r2 + -102r + 210 = 0 Reorder the terms: 210 + -102r + 12r2 = 0 Solving 210 + -102r + 12r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6'. 6(35 + -17r + 2r2) = 0 Factor a trinomial. 6((7 + -2r)(5 + -1r)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + -2r)' equal to zero and attempt to solve: Simplifying 7 + -2r = 0 Solving 7 + -2r = 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 + -2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2r = 0 + -7 -2r = 0 + -7 Combine like terms: 0 + -7 = -7 -2r = -7 Divide each side by '-2'. r = 3.5 Simplifying r = 3.5Subproblem 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 = {3.5, 5}
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