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Simplifying (5m + -2n)(3m + 10n) = 0 Multiply (5m + -2n) * (3m + 10n) (5m * (3m + 10n) + -2n * (3m + 10n)) = 0 ((3m * 5m + 10n * 5m) + -2n * (3m + 10n)) = 0 Reorder the terms: ((50mn + 15m2) + -2n * (3m + 10n)) = 0 ((50mn + 15m2) + -2n * (3m + 10n)) = 0 (50mn + 15m2 + (3m * -2n + 10n * -2n)) = 0 (50mn + 15m2 + (-6mn + -20n2)) = 0 Reorder the terms: (50mn + -6mn + 15m2 + -20n2) = 0 Combine like terms: 50mn + -6mn = 44mn (44mn + 15m2 + -20n2) = 0 Solving 44mn + 15m2 + -20n2 = 0 Solving for variable 'm'. Factor a trinomial. (5m + -2n)(3m + 10n) = 0Subproblem 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 '(3m + 10n)' equal to zero and attempt to solve: Simplifying 3m + 10n = 0 Solving 3m + 10n = 0 Move all terms containing m to the left, all other terms to the right. Add '-10n' to each side of the equation. 3m + 10n + -10n = 0 + -10n Combine like terms: 10n + -10n = 0 3m + 0 = 0 + -10n 3m = 0 + -10n Remove the zero: 3m = -10n Divide each side by '3'. m = -3.333333333n Simplifying m = -3.333333333nSolution
m = {0.4n, -3.333333333n}
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