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Simplifying 15r2 + 10rs + 12rs + 8s2 = 0 Reorder the terms: 10rs + 12rs + 15r2 + 8s2 = 0 Combine like terms: 10rs + 12rs = 22rs 22rs + 15r2 + 8s2 = 0 Solving 22rs + 15r2 + 8s2 = 0 Solving for variable 'r'. Factor a trinomial. (3r + 2s)(5r + 4s) = 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 '(5r + 4s)' equal to zero and attempt to solve: Simplifying 5r + 4s = 0 Solving 5r + 4s = 0 Move all terms containing r to the left, all other terms to the right. Add '-4s' to each side of the equation. 5r + 4s + -4s = 0 + -4s Combine like terms: 4s + -4s = 0 5r + 0 = 0 + -4s 5r = 0 + -4s Remove the zero: 5r = -4s Divide each side by '5'. r = -0.8s Simplifying r = -0.8sSolution
r = {-0.6666666667s, -0.8s}
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