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Simplifying 20r2s + -13rs + -15s = 0 Reorder the terms: -13rs + 20r2s + -15s = 0 Solving -13rs + 20r2s + -15s = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 's'. s(-13r + 20r2 + -15) = 0 Factor a trinomial. s((4r + -5)(5r + 3)) = 0Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. s + -1s = 0 + -1s Remove the zero: 0 = -1s Simplifying 0 = -1s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(4r + -5)' equal to zero and attempt to solve: Simplifying 4r + -5 = 0 Reorder the terms: -5 + 4r = 0 Solving -5 + 4r = 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 + 4r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4r = 0 + 5 4r = 0 + 5 Combine like terms: 0 + 5 = 5 4r = 5 Divide each side by '4'. r = 1.25 Simplifying r = 1.25Subproblem 3
Set the factor '(5r + 3)' equal to zero and attempt to solve: Simplifying 5r + 3 = 0 Reorder the terms: 3 + 5r = 0 Solving 3 + 5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5r = 0 + -3 5r = 0 + -3 Combine like terms: 0 + -3 = -3 5r = -3 Divide each side by '5'. r = -0.6 Simplifying r = -0.6Solution
r = {1.25, -0.6}
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