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Simplifying 0 = 15m2 + mn + -2n2 Reorder the terms: 0 = mn + 15m2 + -2n2 Solving 0 = mn + 15m2 + -2n2 Solving for variable 'm'. Remove the zero: -1mn + -15m2 + 2n2 = mn + 15m2 + -2n2 + -1mn + -15m2 + 2n2 Reorder the terms: -1mn + -15m2 + 2n2 = mn + -1mn + 15m2 + -15m2 + -2n2 + 2n2 Combine like terms: mn + -1mn = 0 -1mn + -15m2 + 2n2 = 0 + 15m2 + -15m2 + -2n2 + 2n2 -1mn + -15m2 + 2n2 = 15m2 + -15m2 + -2n2 + 2n2 Combine like terms: 15m2 + -15m2 = 0 -1mn + -15m2 + 2n2 = 0 + -2n2 + 2n2 -1mn + -15m2 + 2n2 = -2n2 + 2n2 Combine like terms: -2n2 + 2n2 = 0 -1mn + -15m2 + 2n2 = 0 Factor a trinomial. (-5m + -2n)(3m + -1n) = 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 + -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 = 0.3333333333nSolution
m = {-0.4n, 0.3333333333n}
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