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Simplifying 2Ln(x) + Ln(x + -1) = Ln(-2x2 + 5x + -3) Multiply nL * x 2nxL + Ln(x + -1) = Ln(-2x2 + 5x + -3) Reorder the terms: 2nxL + nL(-1 + x) = Ln(-2x2 + 5x + -3) 2nxL + (-1 * nL + x * nL) = Ln(-2x2 + 5x + -3) 2nxL + (-1nL + nxL) = Ln(-2x2 + 5x + -3) Reorder the terms: -1nL + 2nxL + nxL = Ln(-2x2 + 5x + -3) Combine like terms: 2nxL + nxL = 3nxL -1nL + 3nxL = Ln(-2x2 + 5x + -3) Reorder the terms: -1nL + 3nxL = nL(-3 + 5x + -2x2) -1nL + 3nxL = (-3 * nL + 5x * nL + -2x2 * nL) -1nL + 3nxL = (-3nL + 5nxL + -2nx2L) Solving -1nL + 3nxL = -3nL + 5nxL + -2nx2L Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3nL' to each side of the equation. -1nL + 3nL + 3nxL = -3nL + 5nxL + 3nL + -2nx2L Combine like terms: -1nL + 3nL = 2nL 2nL + 3nxL = -3nL + 5nxL + 3nL + -2nx2L Reorder the terms: 2nL + 3nxL = -3nL + 3nL + 5nxL + -2nx2L Combine like terms: -3nL + 3nL = 0 2nL + 3nxL = 0 + 5nxL + -2nx2L 2nL + 3nxL = 5nxL + -2nx2L Add '-5nxL' to each side of the equation. 2nL + 3nxL + -5nxL = 5nxL + -5nxL + -2nx2L Combine like terms: 3nxL + -5nxL = -2nxL 2nL + -2nxL = 5nxL + -5nxL + -2nx2L Combine like terms: 5nxL + -5nxL = 0 2nL + -2nxL = 0 + -2nx2L 2nL + -2nxL = -2nx2L Add '2nx2L' to each side of the equation. 2nL + -2nxL + 2nx2L = -2nx2L + 2nx2L Combine like terms: -2nx2L + 2nx2L = 0 2nL + -2nxL + 2nx2L = 0 Factor out the Greatest Common Factor (GCF), '2nL'. 2nL(1 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'nL' equal to zero and attempt to solve: Simplifying nL = 0 Solving nL = 0 Move all terms containing n to the left, all other terms to the right. Simplifying nL = 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 '(1 + -1x + x2)' equal to zero and attempt to solve: Simplifying 1 + -1x + x2 = 0 Solving 1 + -1x + x2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x + x2 = 0 + -1 -1x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x + x2 = -1 Add 'x' to each side of the equation. -1x + x + x2 = -1 + x Combine like terms: -1x + x = 0 0 + x2 = -1 + x x2 = -1 + x Add '-1x2' to each side of the equation. x2 + -1x2 = -1 + x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -1 + x + -1x2 Simplifying 0 = -1 + x + -1x2 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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