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Simplifying (5r + -3s)(5r + -4s) = 0 Multiply (5r + -3s) * (5r + -4s) (5r * (5r + -4s) + -3s * (5r + -4s)) = 0 ((5r * 5r + -4s * 5r) + -3s * (5r + -4s)) = 0 Reorder the terms: ((-20rs + 25r2) + -3s * (5r + -4s)) = 0 ((-20rs + 25r2) + -3s * (5r + -4s)) = 0 (-20rs + 25r2 + (5r * -3s + -4s * -3s)) = 0 (-20rs + 25r2 + (-15rs + 12s2)) = 0 Reorder the terms: (-20rs + -15rs + 25r2 + 12s2) = 0 Combine like terms: -20rs + -15rs = -35rs (-35rs + 25r2 + 12s2) = 0 Solving -35rs + 25r2 + 12s2 = 0 Solving for variable 'r'. Factor a trinomial. (5r + -4s)(5r + -3s) = 0Subproblem 1
Set the factor '(5r + -4s)' equal to zero and attempt to solve: Simplifying 5r + -4s = 0 Solving 5r + -4s = 0 Move all terms containing r to the left, all other terms to the right. Add '4s' to each side of the equation. 5r + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 5r + 0 = 0 + 4s 5r = 0 + 4s Remove the zero: 5r = 4s Divide each side by '5'. r = 0.8s Simplifying r = 0.8sSubproblem 2
Set the factor '(5r + -3s)' equal to zero and attempt to solve: Simplifying 5r + -3s = 0 Solving 5r + -3s = 0 Move all terms containing r to the left, all other terms to the right. Add '3s' to each side of the equation. 5r + -3s + 3s = 0 + 3s Combine like terms: -3s + 3s = 0 5r + 0 = 0 + 3s 5r = 0 + 3s Remove the zero: 5r = 3s Divide each side by '5'. r = 0.6s Simplifying r = 0.6sSolution
r = {0.8s, 0.6s}
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