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Simplifying 42r2 + -318r + -540 = 0 Reorder the terms: -540 + -318r + 42r2 = 0 Solving -540 + -318r + 42r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6'. 6(-90 + -53r + 7r2) = 0 Factor a trinomial. 6((-10 + -7r)(9 + -1r)) = 0 Ignore the factor 6.Subproblem 1
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 = -1.428571429Subproblem 2
Set the factor '(9 + -1r)' equal to zero and attempt to solve: Simplifying 9 + -1r = 0 Solving 9 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1r = 0 + -9 -1r = 0 + -9 Combine like terms: 0 + -9 = -9 -1r = -9 Divide each side by '-1'. r = 9 Simplifying r = 9Solution
r = {-1.428571429, 9}
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