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Simplifying 3r2 = 30r + -63 Reorder the terms: 3r2 = -63 + 30r Solving 3r2 = -63 + 30r Solving for variable 'r'. Reorder the terms: 63 + -30r + 3r2 = -63 + 30r + 63 + -30r Reorder the terms: 63 + -30r + 3r2 = -63 + 63 + 30r + -30r Combine like terms: -63 + 63 = 0 63 + -30r + 3r2 = 0 + 30r + -30r 63 + -30r + 3r2 = 30r + -30r Combine like terms: 30r + -30r = 0 63 + -30r + 3r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(21 + -10r + r2) = 0 Factor a trinomial. 3((3 + -1r)(7 + -1r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Subproblem 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 = {3, 7}
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