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Simplifying 9m3n + 3m2n + 6mn = 0 Reorder the terms: 6mn + 3m2n + 9m3n = 0 Solving 6mn + 3m2n + 9m3n = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3mn'. 3mn(2 + m + 3m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'mn' equal to zero and attempt to solve: Simplifying mn = 0 Solving mn = 0 Move all terms containing m to the left, all other terms to the right. Simplifying mn = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + m + 3m2)' equal to zero and attempt to solve: Simplifying 2 + m + 3m2 = 0 Solving 2 + m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 0.3333333333m + m2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 0.3333333333m + -0.6666666667 + m2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 0.3333333333m + m2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 0.3333333333m + m2 = 0 + -0.6666666667 0.3333333333m + m2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 0.3333333333m + m2 = -0.6666666667 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333m + 0.25 + m2 = -0.6666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333m + m2 = -0.6666666667 + 0.25 Combine like terms: -0.6666666667 + 0.25 = -0.4166666667 0.25 + 0.3333333333m + m2 = -0.4166666667 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = -0.4166666667 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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