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Simplifying 30m2 + 123mn + -54n2 = 0 Reorder the terms: 123mn + 30m2 + -54n2 = 0 Solving 123mn + 30m2 + -54n2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3'. 3(41mn + 10m2 + -18n2) = 0 Factor a trinomial. 3((5m + -2n)(2m + 9n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5m + -2n)' equal to zero and attempt to solve: Simplifying 5m + -2n = 0 Solving 5m + -2n = 0 Move all terms containing m to the left, all other terms to the right. Add '2n' to each side of the equation. 5m + -2n + 2n = 0 + 2n Combine like terms: -2n + 2n = 0 5m + 0 = 0 + 2n 5m = 0 + 2n Remove the zero: 5m = 2n Divide each side by '5'. m = 0.4n Simplifying m = 0.4nSubproblem 2
Set the factor '(2m + 9n)' equal to zero and attempt to solve: Simplifying 2m + 9n = 0 Solving 2m + 9n = 0 Move all terms containing m to the left, all other terms to the right. Add '-9n' to each side of the equation. 2m + 9n + -9n = 0 + -9n Combine like terms: 9n + -9n = 0 2m + 0 = 0 + -9n 2m = 0 + -9n Remove the zero: 2m = -9n Divide each side by '2'. m = -4.5n Simplifying m = -4.5nSolution
m = {0.4n, -4.5n}
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