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Simplifying 20m2 + -43mn + 21n2 = 0 Reorder the terms: -43mn + 20m2 + 21n2 = 0 Solving -43mn + 20m2 + 21n2 = 0 Solving for variable 'm'. Factor a trinomial. (5m + -7n)(4m + -3n) = 0Subproblem 1
Set the factor '(5m + -7n)' equal to zero and attempt to solve: Simplifying 5m + -7n = 0 Solving 5m + -7n = 0 Move all terms containing m to the left, all other terms to the right. Add '7n' to each side of the equation. 5m + -7n + 7n = 0 + 7n Combine like terms: -7n + 7n = 0 5m + 0 = 0 + 7n 5m = 0 + 7n Remove the zero: 5m = 7n Divide each side by '5'. m = 1.4n Simplifying m = 1.4nSubproblem 2
Set the factor '(4m + -3n)' equal to zero and attempt to solve: Simplifying 4m + -3n = 0 Solving 4m + -3n = 0 Move all terms containing m to the left, all other terms to the right. Add '3n' to each side of the equation. 4m + -3n + 3n = 0 + 3n Combine like terms: -3n + 3n = 0 4m + 0 = 0 + 3n 4m = 0 + 3n Remove the zero: 4m = 3n Divide each side by '4'. m = 0.75n Simplifying m = 0.75nSolution
m = {1.4n, 0.75n}
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