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Simplifying 4xln(x + 1) + -8x = 0 Reorder the terms: 4lnx(1 + x) + -8x = 0 (1 * 4lnx + x * 4lnx) + -8x = 0 (4lnx + 4lnx2) + -8x = 0 Solving 4lnx + 4lnx2 + -8x = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8x' to each side of the equation. 4lnx + 4lnx2 + -8x + 8x = 0 + 8x Combine like terms: -8x + 8x = 0 4lnx + 4lnx2 + 0 = 0 + 8x 4lnx + 4lnx2 = 0 + 8x Remove the zero: 4lnx + 4lnx2 = 8x Combine like terms: 8x + -8x = 0 4lnx + 4lnx2 + -8x = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(ln + lnx + -2) = 0 Ignore the factor 4.Subproblem 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 '(ln + lnx + -2)' equal to zero and attempt to solve: Simplifying ln + lnx + -2 = 0 Reorder the terms: -2 + ln + lnx = 0 Solving -2 + ln + lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + ln + 2 + lnx = 0 + 2 Reorder the terms: -2 + 2 + ln + lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + ln + lnx = 0 + 2 ln + lnx = 0 + 2 Combine like terms: 0 + 2 = 2 ln + lnx = 2 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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