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Simplifying 14m2 + 35mn + -21n2 = 0 Reorder the terms: 35mn + 14m2 + -21n2 = 0 Solving 35mn + 14m2 + -21n2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '7'. 7(5mn + 2m2 + -3n2) = 0 Factor a trinomial. 7((2m + -1n)(m + 3n)) = 0 Ignore the factor 7.Subproblem 1
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 = 0.5nSubproblem 2
Set the factor '(m + 3n)' equal to zero and attempt to solve: Simplifying m + 3n = 0 Solving m + 3n = 0 Move all terms containing m to the left, all other terms to the right. Add '-3n' to each side of the equation. m + 3n + -3n = 0 + -3n Combine like terms: 3n + -3n = 0 m + 0 = 0 + -3n m = 0 + -3n Remove the zero: m = -3n Simplifying m = -3nSolution
m = {0.5n, -3n}
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