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Simplifying 42r2 + 228r + 240 = 0 Reorder the terms: 240 + 228r + 42r2 = 0 Solving 240 + 228r + 42r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6'. 6(40 + 38r + 7r2) = 0 Factor a trinomial. 6((4 + r)(10 + 7r)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + r)' equal to zero and attempt to solve: Simplifying 4 + r = 0 Solving 4 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + r = 0 + -4 r = 0 + -4 Combine like terms: 0 + -4 = -4 r = -4 Simplifying r = -4Subproblem 2
Set the factor '(10 + 7r)' equal to zero and attempt to solve: Simplifying 10 + 7r = 0 Solving 10 + 7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 7r = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 7r = 0 + -10 7r = 0 + -10 Combine like terms: 0 + -10 = -10 7r = -10 Divide each side by '7'. r = -1.428571429 Simplifying r = -1.428571429Solution
r = {-4, -1.428571429}
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