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Simplifying 0 = 6m2 + 5mn + -4n2 Reorder the terms: 0 = 5mn + 6m2 + -4n2 Solving 0 = 5mn + 6m2 + -4n2 Solving for variable 'm'. Remove the zero: -5mn + -6m2 + 4n2 = 5mn + 6m2 + -4n2 + -5mn + -6m2 + 4n2 Reorder the terms: -5mn + -6m2 + 4n2 = 5mn + -5mn + 6m2 + -6m2 + -4n2 + 4n2 Combine like terms: 5mn + -5mn = 0 -5mn + -6m2 + 4n2 = 0 + 6m2 + -6m2 + -4n2 + 4n2 -5mn + -6m2 + 4n2 = 6m2 + -6m2 + -4n2 + 4n2 Combine like terms: 6m2 + -6m2 = 0 -5mn + -6m2 + 4n2 = 0 + -4n2 + 4n2 -5mn + -6m2 + 4n2 = -4n2 + 4n2 Combine like terms: -4n2 + 4n2 = 0 -5mn + -6m2 + 4n2 = 0 Factor a trinomial. (-3m + -4n)(2m + -1n) = 0Subproblem 1
Set the factor '(-3m + -4n)' equal to zero and attempt to solve: Simplifying -3m + -4n = 0 Solving -3m + -4n = 0 Move all terms containing m to the left, all other terms to the right. Add '4n' to each side of the equation. -3m + -4n + 4n = 0 + 4n Combine like terms: -4n + 4n = 0 -3m + 0 = 0 + 4n -3m = 0 + 4n Remove the zero: -3m = 4n Divide each side by '-3'. m = -1.333333333n Simplifying m = -1.333333333nSubproblem 2
Set the factor '(2m + -1n)' equal to zero and attempt to solve: Simplifying 2m + -1n = 0 Solving 2m + -1n = 0 Move all terms containing m to the left, all other terms to the right. Add 'n' to each side of the equation. 2m + -1n + n = 0 + n Combine like terms: -1n + n = 0 2m + 0 = 0 + n 2m = 0 + n Remove the zero: 2m = n Divide each side by '2'. m = 0.5n Simplifying m = 0.5nSolution
m = {-1.333333333n, 0.5n}
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