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Simplifying ln(x)(2 + -3x) + ln(x)(x + 4) = 0 Multiply ln * x lnx(2 + -3x) + ln(x)(x + 4) = 0 (2 * lnx + -3x * lnx) + ln(x)(x + 4) = 0 (2lnx + -3lnx2) + ln(x)(x + 4) = 0 Reorder the terms: 2lnx + -3lnx2 + ln * x(4 + x) = 0 Multiply ln * x 2lnx + -3lnx2 + lnx(4 + x) = 0 2lnx + -3lnx2 + (4 * lnx + x * lnx) = 0 2lnx + -3lnx2 + (4lnx + lnx2) = 0 Reorder the terms: 2lnx + 4lnx + -3lnx2 + lnx2 = 0 Combine like terms: 2lnx + 4lnx = 6lnx 6lnx + -3lnx2 + lnx2 = 0 Combine like terms: -3lnx2 + lnx2 = -2lnx2 6lnx + -2lnx2 = 0 Solving 6lnx + -2lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2lnx'. 2lnx(3 + -1x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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