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Simplifying 12r2 + 9rs + 20rs + 15s2 = 0 Reorder the terms: 9rs + 20rs + 12r2 + 15s2 = 0 Combine like terms: 9rs + 20rs = 29rs 29rs + 12r2 + 15s2 = 0 Solving 29rs + 12r2 + 15s2 = 0 Solving for variable 'r'. Factor a trinomial. (4r + 3s)(3r + 5s) = 0Subproblem 1
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 = -0.75sSubproblem 2
Set the factor '(3r + 5s)' equal to zero and attempt to solve: Simplifying 3r + 5s = 0 Solving 3r + 5s = 0 Move all terms containing r to the left, all other terms to the right. Add '-5s' to each side of the equation. 3r + 5s + -5s = 0 + -5s Combine like terms: 5s + -5s = 0 3r + 0 = 0 + -5s 3r = 0 + -5s Remove the zero: 3r = -5s Divide each side by '3'. r = -1.666666667s Simplifying r = -1.666666667sSolution
r = {-0.75s, -1.666666667s}
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