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Simplifying 6r2 + 31r + 35 = 0 Reorder the terms: 35 + 31r + 6r2 = 0 Solving 35 + 31r + 6r2 = 0 Solving for variable 'r'. Factor a trinomial. (7 + 2r)(5 + 3r) = 0Subproblem 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 + 3r)' equal to zero and attempt to solve: Simplifying 5 + 3r = 0 Solving 5 + 3r = 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 + 3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3r = 0 + -5 3r = 0 + -5 Combine like terms: 0 + -5 = -5 3r = -5 Divide each side by '3'. r = -1.666666667 Simplifying r = -1.666666667Solution
r = {-3.5, -1.666666667}
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