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Simplifying 12r2 + 5rs + -3s2 = 0 Reorder the terms: 5rs + 12r2 + -3s2 = 0 Solving 5rs + 12r2 + -3s2 = 0 Solving for variable 'r'. Factor a trinomial. (3r + -1s)(4r + 3s) = 0Subproblem 1
Set the factor '(3r + -1s)' equal to zero and attempt to solve: Simplifying 3r + -1s = 0 Solving 3r + -1s = 0 Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. 3r + -1s + s = 0 + s Combine like terms: -1s + s = 0 3r + 0 = 0 + s 3r = 0 + s Remove the zero: 3r = s Divide each side by '3'. r = 0.3333333333s Simplifying r = 0.3333333333sSubproblem 2
Set the factor '(4r + 3s)' equal to zero and attempt to solve: Simplifying 4r + 3s = 0 Solving 4r + 3s = 0 Move all terms containing r to the left, all other terms to the right. Add '-3s' to each side of the equation. 4r + 3s + -3s = 0 + -3s Combine like terms: 3s + -3s = 0 4r + 0 = 0 + -3s 4r = 0 + -3s Remove the zero: 4r = -3s Divide each side by '4'. r = -0.75s Simplifying r = -0.75sSolution
r = {0.3333333333s, -0.75s}
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