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Simplifying (3r + s)(r + -3s) = 0 Multiply (3r + s) * (r + -3s) (3r * (r + -3s) + s(r + -3s)) = 0 ((r * 3r + -3s * 3r) + s(r + -3s)) = 0 Reorder the terms: ((-9rs + 3r2) + s(r + -3s)) = 0 ((-9rs + 3r2) + s(r + -3s)) = 0 (-9rs + 3r2 + (r * s + -3s * s)) = 0 (-9rs + 3r2 + (rs + -3s2)) = 0 Reorder the terms: (-9rs + rs + 3r2 + -3s2) = 0 Combine like terms: -9rs + rs = -8rs (-8rs + 3r2 + -3s2) = 0 Solving -8rs + 3r2 + -3s2 = 0 Solving for variable 'r'. Factor a trinomial. (r + -3s)(3r + s) = 0Subproblem 1
Set the factor '(r + -3s)' equal to zero and attempt to solve: Simplifying r + -3s = 0 Solving r + -3s = 0 Move all terms containing r to the left, all other terms to the right. Add '3s' to each side of the equation. r + -3s + 3s = 0 + 3s Combine like terms: -3s + 3s = 0 r + 0 = 0 + 3s r = 0 + 3s Remove the zero: r = 3s Simplifying r = 3sSubproblem 2
Set the factor '(3r + s)' equal to zero and attempt to solve: Simplifying 3r + s = 0 Solving 3r + s = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. 3r + s + -1s = 0 + -1s Combine like terms: s + -1s = 0 3r + 0 = 0 + -1s 3r = 0 + -1s Remove the zero: 3r = -1s Divide each side by '3'. r = -0.3333333333s Simplifying r = -0.3333333333sSolution
r = {3s, -0.3333333333s}
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