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Simplifying 3r2 + 13rs + 12s2 = 0 Reorder the terms: 13rs + 3r2 + 12s2 = 0 Solving 13rs + 3r2 + 12s2 = 0 Solving for variable 'r'. Factor a trinomial. (3r + 4s)(r + 3s) = 0Subproblem 1
Set the factor '(3r + 4s)' equal to zero and attempt to solve: Simplifying 3r + 4s = 0 Solving 3r + 4s = 0 Move all terms containing r to the left, all other terms to the right. Add '-4s' to each side of the equation. 3r + 4s + -4s = 0 + -4s Combine like terms: 4s + -4s = 0 3r + 0 = 0 + -4s 3r = 0 + -4s Remove the zero: 3r = -4s Divide each side by '3'. r = -1.333333333s Simplifying r = -1.333333333sSubproblem 2
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 = -3sSolution
r = {-1.333333333s, -3s}
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