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Simplifying 6r2 = 210 + 12r Solving 6r2 = 210 + 12r Solving for variable 'r'. Reorder the terms: -210 + -12r + 6r2 = 210 + 12r + -210 + -12r Reorder the terms: -210 + -12r + 6r2 = 210 + -210 + 12r + -12r Combine like terms: 210 + -210 = 0 -210 + -12r + 6r2 = 0 + 12r + -12r -210 + -12r + 6r2 = 12r + -12r Combine like terms: 12r + -12r = 0 -210 + -12r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-35 + -2r + r2) = 0 Factor a trinomial. 6((-5 + -1r)(7 + -1r)) = 0 Ignore the factor 6.Subproblem 1
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 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 = 7Solution
r = {-5, 7}
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