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Simplifying 6r2 + 15rs + 8rs + 20s2 = 0 Reorder the terms: 15rs + 8rs + 6r2 + 20s2 = 0 Combine like terms: 15rs + 8rs = 23rs 23rs + 6r2 + 20s2 = 0 Solving 23rs + 6r2 + 20s2 = 0 Solving for variable 'r'. Factor a trinomial. (3r + 4s)(2r + 5s) = 0Subproblem 1
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 = -1.333333333sSubproblem 2
Set the factor '(2r + 5s)' equal to zero and attempt to solve: Simplifying 2r + 5s = 0 Solving 2r + 5s = 0 Move all terms containing r to the left, all other terms to the right. Add '-5s' to each side of the equation. 2r + 5s + -5s = 0 + -5s Combine like terms: 5s + -5s = 0 2r + 0 = 0 + -5s 2r = 0 + -5s Remove the zero: 2r = -5s Divide each side by '2'. r = -2.5s Simplifying r = -2.5sSolution
r = {-1.333333333s, -2.5s}
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