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Simplifying 12r2 + 8rs + 9rs + 6s2 = 0 Reorder the terms: 8rs + 9rs + 12r2 + 6s2 = 0 Combine like terms: 8rs + 9rs = 17rs 17rs + 12r2 + 6s2 = 0 Solving 17rs + 12r2 + 6s2 = 0 Solving for variable 'r'. Factor a trinomial. (3r + 2s)(4r + 3s) = 0Subproblem 1
Set the factor '(3r + 2s)' equal to zero and attempt to solve: Simplifying 3r + 2s = 0 Solving 3r + 2s = 0 Move all terms containing r to the left, all other terms to the right. Add '-2s' to each side of the equation. 3r + 2s + -2s = 0 + -2s Combine like terms: 2s + -2s = 0 3r + 0 = 0 + -2s 3r = 0 + -2s Remove the zero: 3r = -2s Divide each side by '3'. r = -0.6666666667s Simplifying r = -0.6666666667sSubproblem 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 = {-0.6666666667s, -0.75s}
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