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