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Simplifying 3r2 + 14r + 16 = 0 Reorder the terms: 16 + 14r + 3r2 = 0 Solving 16 + 14r + 3r2 = 0 Solving for variable 'r'. Factor a trinomial. (8 + 3r)(2 + r) = 0Subproblem 1
Set the factor '(8 + 3r)' equal to zero and attempt to solve: Simplifying 8 + 3r = 0 Solving 8 + 3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3r = 0 + -8 3r = 0 + -8 Combine like terms: 0 + -8 = -8 3r = -8 Divide each side by '3'. r = -2.666666667 Simplifying r = -2.666666667Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve: Simplifying 2 + r = 0 Solving 2 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + r = 0 + -2 r = 0 + -2 Combine like terms: 0 + -2 = -2 r = -2 Simplifying r = -2Solution
r = {-2.666666667, -2}
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