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Simplifying 90m2 + 21mn + -6n2 = 0 Reorder the terms: 21mn + 90m2 + -6n2 = 0 Solving 21mn + 90m2 + -6n2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3'. 3(7mn + 30m2 + -2n2) = 0 Factor a trinomial. 3((6m + -1n)(5m + 2n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6m + -1n)' equal to zero and attempt to solve: Simplifying 6m + -1n = 0 Solving 6m + -1n = 0 Move all terms containing m to the left, all other terms to the right. Add 'n' to each side of the equation. 6m + -1n + n = 0 + n Combine like terms: -1n + n = 0 6m + 0 = 0 + n 6m = 0 + n Remove the zero: 6m = n Divide each side by '6'. m = 0.1666666667n Simplifying m = 0.1666666667nSubproblem 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 = {0.1666666667n, -0.4n}
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