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Simplifying 6xln(1 + x) + -1x = 0 (1 * 6lnx + x * 6lnx) + -1x = 0 (6lnx + 6lnx2) + -1x = 0 Solving 6lnx + 6lnx2 + -1x = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'x' to each side of the equation. 6lnx + 6lnx2 + -1x + x = 0 + x Combine like terms: -1x + x = 0 6lnx + 6lnx2 + 0 = 0 + x 6lnx + 6lnx2 = 0 + x Remove the zero: 6lnx + 6lnx2 = x Combine like terms: x + -1x = 0 6lnx + 6lnx2 + -1x = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(6ln + 6lnx + -1) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(6ln + 6lnx + -1)' equal to zero and attempt to solve: Simplifying 6ln + 6lnx + -1 = 0 Reorder the terms: -1 + 6ln + 6lnx = 0 Solving -1 + 6ln + 6lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 6ln + 1 + 6lnx = 0 + 1 Reorder the terms: -1 + 1 + 6ln + 6lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6ln + 6lnx = 0 + 1 6ln + 6lnx = 0 + 1 Combine like terms: 0 + 1 = 1 6ln + 6lnx = 1 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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