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Simplifying 4n2 + -20nm + 24m2 = 0 Reorder the terms: -20mn + 24m2 + 4n2 = 0 Solving -20mn + 24m2 + 4n2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5mn + 6m2 + n2) = 0 Factor a trinomial. 4((2m + -1n)(3m + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2m + -1n)' equal to zero and attempt to solve: Simplifying 2m + -1n = 0 Solving 2m + -1n = 0 Move all terms containing m to the left, all other terms to the right. Add 'n' to each side of the equation. 2m + -1n + n = 0 + n Combine like terms: -1n + n = 0 2m + 0 = 0 + n 2m = 0 + n Remove the zero: 2m = n Divide each side by '2'. m = 0.5n Simplifying m = 0.5nSubproblem 2
Set the factor '(3m + -1n)' equal to zero and attempt to solve: Simplifying 3m + -1n = 0 Solving 3m + -1n = 0 Move all terms containing m to the left, all other terms to the right. Add 'n' to each side of the equation. 3m + -1n + n = 0 + n Combine like terms: -1n + n = 0 3m + 0 = 0 + n 3m = 0 + n Remove the zero: 3m = n Divide each side by '3'. m = 0.3333333333n Simplifying m = 0.3333333333nSolution
m = {0.5n, 0.3333333333n}
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