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Simplifying 24m2 + 128mn + -96n2 = 0 Reorder the terms: 128mn + 24m2 + -96n2 = 0 Solving 128mn + 24m2 + -96n2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '8'. 8(16mn + 3m2 + -12n2) = 0 Factor a trinomial. 8((3m + -2n)(m + 6n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3m + -2n)' equal to zero and attempt to solve: Simplifying 3m + -2n = 0 Solving 3m + -2n = 0 Move all terms containing m to the left, all other terms to the right. Add '2n' to each side of the equation. 3m + -2n + 2n = 0 + 2n Combine like terms: -2n + 2n = 0 3m + 0 = 0 + 2n 3m = 0 + 2n Remove the zero: 3m = 2n Divide each side by '3'. m = 0.6666666667n Simplifying m = 0.6666666667nSubproblem 2
Set the factor '(m + 6n)' equal to zero and attempt to solve: Simplifying m + 6n = 0 Solving m + 6n = 0 Move all terms containing m to the left, all other terms to the right. Add '-6n' to each side of the equation. m + 6n + -6n = 0 + -6n Combine like terms: 6n + -6n = 0 m + 0 = 0 + -6n m = 0 + -6n Remove the zero: m = -6n Simplifying m = -6nSolution
m = {0.6666666667n, -6n}
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