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Simplifying n(y) = ln(ax2 + bx + c) Multiply n * y ny = ln(ax2 + bx + c) ny = (ax2 * ln + bx * ln + c * ln) ny = (alnx2 + blnx + cln) Solving ny = alnx2 + blnx + cln Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1alnx2' to each side of the equation. -1alnx2 + ny = alnx2 + blnx + -1alnx2 + cln Reorder the terms: -1alnx2 + ny = alnx2 + -1alnx2 + blnx + cln Combine like terms: alnx2 + -1alnx2 = 0 -1alnx2 + ny = 0 + blnx + cln -1alnx2 + ny = blnx + cln Add '-1blnx' to each side of the equation. -1alnx2 + -1blnx + ny = blnx + -1blnx + cln Combine like terms: blnx + -1blnx = 0 -1alnx2 + -1blnx + ny = 0 + cln -1alnx2 + -1blnx + ny = cln Add '-1cln' to each side of the equation. -1alnx2 + -1blnx + -1cln + ny = cln + -1cln Combine like terms: cln + -1cln = 0 -1alnx2 + -1blnx + -1cln + ny = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-1alx2 + -1blx + -1cl + y) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-1alx2 + -1blx + -1cl + y)' equal to zero and attempt to solve: Simplifying -1alx2 + -1blx + -1cl + y = 0 Solving -1alx2 + -1blx + -1cl + y = 0 Move all terms containing n to the left, all other terms to the right. Add 'alx2' to each side of the equation. -1alx2 + -1blx + -1cl + alx2 + y = 0 + alx2 Reorder the terms: -1alx2 + alx2 + -1blx + -1cl + y = 0 + alx2 Combine like terms: -1alx2 + alx2 = 0 0 + -1blx + -1cl + y = 0 + alx2 -1blx + -1cl + y = 0 + alx2 Remove the zero: -1blx + -1cl + y = alx2 Add 'blx' to each side of the equation. -1blx + -1cl + blx + y = alx2 + blx Reorder the terms: -1blx + blx + -1cl + y = alx2 + blx Combine like terms: -1blx + blx = 0 0 + -1cl + y = alx2 + blx -1cl + y = alx2 + blx Add 'cl' to each side of the equation. -1cl + cl + y = alx2 + blx + cl Combine like terms: -1cl + cl = 0 0 + y = alx2 + blx + cl y = alx2 + blx + cl Add '-1y' to each side of the equation. y + -1y = alx2 + blx + cl + -1y Combine like terms: y + -1y = 0 0 = alx2 + blx + cl + -1y Simplifying 0 = alx2 + blx + cl + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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