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Simplifying 2r2 + rs + -3s2 = 0 Reorder the terms: rs + 2r2 + -3s2 = 0 Solving rs + 2r2 + -3s2 = 0 Solving for variable 'r'. Factor a trinomial. (r + -1s)(2r + 3s) = 0Subproblem 1
Set the factor '(r + -1s)' equal to zero and attempt to solve: Simplifying r + -1s = 0 Solving r + -1s = 0 Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. r + -1s + s = 0 + s Combine like terms: -1s + s = 0 r + 0 = 0 + s r = 0 + s Remove the zero: r = s Simplifying r = sSubproblem 2
Set the factor '(2r + 3s)' equal to zero and attempt to solve: Simplifying 2r + 3s = 0 Solving 2r + 3s = 0 Move all terms containing r to the left, all other terms to the right. Add '-3s' to each side of the equation. 2r + 3s + -3s = 0 + -3s Combine like terms: 3s + -3s = 0 2r + 0 = 0 + -3s 2r = 0 + -3s Remove the zero: 2r = -3s Divide each side by '2'. r = -1.5s Simplifying r = -1.5sSolution
r = {s, -1.5s}
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