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Simplifying 12r2 + 23rs + 10s2 = 12rs + 15rs + 8rs + 10s2 Reorder the terms: 23rs + 12r2 + 10s2 = 12rs + 15rs + 8rs + 10s2 Combine like terms: 12rs + 15rs = 27rs 23rs + 12r2 + 10s2 = 27rs + 8rs + 10s2 Combine like terms: 27rs + 8rs = 35rs 23rs + 12r2 + 10s2 = 35rs + 10s2 Add '-10s2' to each side of the equation. 23rs + 12r2 + 10s2 + -10s2 = 35rs + 10s2 + -10s2 Combine like terms: 10s2 + -10s2 = 0 23rs + 12r2 + 0 = 35rs + 10s2 + -10s2 23rs + 12r2 = 35rs + 10s2 + -10s2 Combine like terms: 10s2 + -10s2 = 0 23rs + 12r2 = 35rs + 0 23rs + 12r2 = 35rs Solving 23rs + 12r2 = 35rs Solving for variable 'r'. Reorder the terms: 23rs + -35rs + 12r2 = 35rs + -35rs Combine like terms: 23rs + -35rs = -12rs -12rs + 12r2 = 35rs + -35rs Combine like terms: 35rs + -35rs = 0 -12rs + 12r2 = 0 Factor out the Greatest Common Factor (GCF), '12r'. 12r(-1s + r) = 0 Ignore the factor 12.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(-1s + r)' equal to zero and attempt to solve: Simplifying -1s + r = 0 Reorder the terms: r + -1s = 0 Solving r + -1s = 0 Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. r + -1s + s = 0 + s Combine like terms: -1s + s = 0 r + 0 = 0 + s r = 0 + s Remove the zero: r = s Simplifying r = sSolution
r = {0, s}
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