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Simplifying 12r2 + 93r + 126 = 0 Reorder the terms: 126 + 93r + 12r2 = 0 Solving 126 + 93r + 12r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3'. 3(42 + 31r + 4r2) = 0 Factor a trinomial. 3((6 + r)(7 + 4r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve: Simplifying 6 + r = 0 Solving 6 + r = 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 + r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + r = 0 + -6 r = 0 + -6 Combine like terms: 0 + -6 = -6 r = -6 Simplifying r = -6Subproblem 2
Set the factor '(7 + 4r)' equal to zero and attempt to solve: Simplifying 7 + 4r = 0 Solving 7 + 4r = 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 + 4r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4r = 0 + -7 4r = 0 + -7 Combine like terms: 0 + -7 = -7 4r = -7 Divide each side by '4'. r = -1.75 Simplifying r = -1.75Solution
r = {-6, -1.75}
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