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Simplifying m4n4 + -81 = 0 Reorder the terms: -81 + m4n4 = 0 Solving -81 + m4n4 = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + m4n4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + m4n4 = 0 + 81 m4n4 = 0 + 81 Combine like terms: 0 + 81 = 81 m4n4 = 81 Divide each side by 'n4'. m4 = 81n-4 Simplifying m4 = 81n-4 Combine like terms: 81n-4 + -81n-4 = 0 m4 + -81n-4 = 0 Factor out the Greatest Common Factor (GCF), 'n-4'. n-4(m4n4 + -81) = 0 Factor a difference between two squares. n-4((m2n2 + 9)(m2n2 + -9)) = 0 Factor a difference between two squares. n-4((m2n2 + 9)((mn + 3)(mn + -3))) = 0Subproblem 1
Set the factor 'n-4' equal to zero and attempt to solve: Simplifying n-4 = 0 Solving n-4 = 0 Move all terms containing m to the left, all other terms to the right. Add '-1n-4' to each side of the equation. n-4 + -1n-4 = 0 + -1n-4 Remove the zero: 0 = -1n-4 Simplifying 0 = -1n-4 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 '(m2n2 + 9)' equal to zero and attempt to solve: Simplifying m2n2 + 9 = 0 Reorder the terms: 9 + m2n2 = 0 Solving 9 + m2n2 = 0 Move all terms containing m to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + m2n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + m2n2 = 0 + -9 m2n2 = 0 + -9 Combine like terms: 0 + -9 = -9 m2n2 = -9 Divide each side by 'n2'. m2 = -9n-2 Simplifying m2 = -9n-2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 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-1Subproblem 4
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 = {-3n-1, 3n-1}
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