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Simplifying 10m2 + -15mn + 4mn + -6n2 = 0 Reorder the terms: -15mn + 4mn + 10m2 + -6n2 = 0 Combine like terms: -15mn + 4mn = -11mn -11mn + 10m2 + -6n2 = 0 Solving -11mn + 10m2 + -6n2 = 0 Solving for variable 'm'. Factor a trinomial. (2m + -3n)(5m + 2n) = 0Subproblem 1
Set the factor '(2m + -3n)' equal to zero and attempt to solve: Simplifying 2m + -3n = 0 Solving 2m + -3n = 0 Move all terms containing m to the left, all other terms to the right. Add '3n' to each side of the equation. 2m + -3n + 3n = 0 + 3n Combine like terms: -3n + 3n = 0 2m + 0 = 0 + 3n 2m = 0 + 3n Remove the zero: 2m = 3n Divide each side by '2'. m = 1.5n Simplifying m = 1.5nSubproblem 2
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 = -0.4nSolution
m = {1.5n, -0.4n}
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