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Simplifying 54r2 + 72r + 24 = 0 Reorder the terms: 24 + 72r + 54r2 = 0 Solving 24 + 72r + 54r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + 12r + 9r2) = 0 Factor a trinomial. 6((2 + 3r)(2 + 3r)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + 3r)' equal to zero and attempt to solve: Simplifying 2 + 3r = 0 Solving 2 + 3r = 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 + 3r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3r = 0 + -2 3r = 0 + -2 Combine like terms: 0 + -2 = -2 3r = -2 Divide each side by '3'. r = -0.6666666667 Simplifying r = -0.6666666667Subproblem 2
Set the factor '(2 + 3r)' equal to zero and attempt to solve: Simplifying 2 + 3r = 0 Solving 2 + 3r = 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 + 3r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3r = 0 + -2 3r = 0 + -2 Combine like terms: 0 + -2 = -2 3r = -2 Divide each side by '3'. r = -0.6666666667 Simplifying r = -0.6666666667Solution
r = {-0.6666666667, -0.6666666667}
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