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Simplifying 15r2 + 20rs + 9rs + 12s2 = 0 Reorder the terms: 20rs + 9rs + 15r2 + 12s2 = 0 Combine like terms: 20rs + 9rs = 29rs 29rs + 15r2 + 12s2 = 0 Solving 29rs + 15r2 + 12s2 = 0 Solving for variable 'r'. Factor a trinomial. (5r + 3s)(3r + 4s) = 0Subproblem 1
Set the factor '(5r + 3s)' equal to zero and attempt to solve: Simplifying 5r + 3s = 0 Solving 5r + 3s = 0 Move all terms containing r to the left, all other terms to the right. Add '-3s' to each side of the equation. 5r + 3s + -3s = 0 + -3s Combine like terms: 3s + -3s = 0 5r + 0 = 0 + -3s 5r = 0 + -3s Remove the zero: 5r = -3s Divide each side by '5'. r = -0.6s Simplifying r = -0.6sSubproblem 2
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 = -1.333333333sSolution
r = {-0.6s, -1.333333333s}
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