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Simplifying 2m2n2 + 2n + -12 = 0 Reorder the terms: -12 + 2m2n2 + 2n = 0 Solving -12 + 2m2n2 + 2n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 2m2n2 + 12 + 2n = 0 + 12 Reorder the terms: -12 + 12 + 2m2n2 + 2n = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2m2n2 + 2n = 0 + 12 2m2n2 + 2n = 0 + 12 Combine like terms: 0 + 12 = 12 2m2n2 + 2n = 12 Add '-2n' to each side of the equation. 2m2n2 + 2n + -2n = 12 + -2n Combine like terms: 2n + -2n = 0 2m2n2 + 0 = 12 + -2n 2m2n2 = 12 + -2n Divide each side by '2n2'. m2 = 6n-2 + -1n-1 Simplifying m2 = 6n-2 + -1n-1 Reorder the terms: m2 + -6n-2 + n-1 = 6n-2 + -6n-2 + -1n-1 + n-1 Combine like terms: 6n-2 + -6n-2 = 0 m2 + -6n-2 + n-1 = 0 + -1n-1 + n-1 m2 + -6n-2 + n-1 = -1n-1 + n-1 Combine like terms: -1n-1 + n-1 = 0 m2 + -6n-2 + n-1 = 0 Factor out the Greatest Common Factor (GCF), 'n-2'. n-2(m2n2 + -6 + n) = 0 Factor a trinomial. n-2((mn + -2)(mn + 3)) = 0Subproblem 1
Set the factor 'n-2' equal to zero and attempt to solve: Simplifying n-2 = 0 Solving n-2 = 0 Move all terms containing m to the left, all other terms to the right. Add '-1n-2' to each side of the equation. n-2 + -1n-2 = 0 + -1n-2 Remove the zero: 0 = -1n-2 Simplifying 0 = -1n-2 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 '(mn + -2)' equal to zero and attempt to solve: Simplifying mn + -2 = 0 Reorder the terms: -2 + mn = 0 Solving -2 + mn = 0 Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + mn = 0 + 2 Combine like terms: -2 + 2 = 0 0 + mn = 0 + 2 mn = 0 + 2 Combine like terms: 0 + 2 = 2 mn = 2 Divide each side by 'n'. m = 2n-1 Simplifying m = 2n-1Subproblem 3
Set the factor '(mn + 3)' equal to zero and attempt to solve: Simplifying mn + 3 = 0 Reorder the terms: 3 + mn = 0 Solving 3 + mn = 0 Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + mn = 0 + -3 Combine like terms: 3 + -3 = 0 0 + mn = 0 + -3 mn = 0 + -3 Combine like terms: 0 + -3 = -3 mn = -3 Divide each side by 'n'. m = -3n-1 Simplifying m = -3n-1Solution
m = {2n-1, -3n-1}
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