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Simplifying (6r + 4s)(6r + 4s) = 0 Multiply (6r + 4s) * (6r + 4s) (6r * (6r + 4s) + 4s * (6r + 4s)) = 0 ((6r * 6r + 4s * 6r) + 4s * (6r + 4s)) = 0 Reorder the terms: ((24rs + 36r2) + 4s * (6r + 4s)) = 0 ((24rs + 36r2) + 4s * (6r + 4s)) = 0 (24rs + 36r2 + (6r * 4s + 4s * 4s)) = 0 (24rs + 36r2 + (24rs + 16s2)) = 0 Reorder the terms: (24rs + 24rs + 36r2 + 16s2) = 0 Combine like terms: 24rs + 24rs = 48rs (48rs + 36r2 + 16s2) = 0 Solving 48rs + 36r2 + 16s2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(12rs + 9r2 + 4s2) = 0 Factor a trinomial. 4((3r + 2s)(3r + 2s)) = 0 Ignore the factor 4.Subproblem 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 '(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 = -0.6666666667sSolution
r = {-0.6666666667s, -0.6666666667s}
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