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Simplifying ln(x2 + -3x + -4) + ln(x2 + -9x + 20) = 0 Reorder the terms: ln(-4 + -3x + x2) + ln(x2 + -9x + 20) = 0 (-4 * ln + -3x * ln + x2 * ln) + ln(x2 + -9x + 20) = 0 (-4ln + -3lnx + lnx2) + ln(x2 + -9x + 20) = 0 Reorder the terms: -4ln + -3lnx + lnx2 + ln(20 + -9x + x2) = 0 -4ln + -3lnx + lnx2 + (20 * ln + -9x * ln + x2 * ln) = 0 -4ln + -3lnx + lnx2 + (20ln + -9lnx + lnx2) = 0 Reorder the terms: -4ln + 20ln + -3lnx + -9lnx + lnx2 + lnx2 = 0 Combine like terms: -4ln + 20ln = 16ln 16ln + -3lnx + -9lnx + lnx2 + lnx2 = 0 Combine like terms: -3lnx + -9lnx = -12lnx 16ln + -12lnx + lnx2 + lnx2 = 0 Combine like terms: lnx2 + lnx2 = 2lnx2 16ln + -12lnx + 2lnx2 = 0 Solving 16ln + -12lnx + 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), '2ln'. 2ln(8 + -6x + x2) = 0 Factor a trinomial. 2ln((2 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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