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Simplifying (-3x + 6) * ln(x + -2) = 0 Reorder the terms: (6 + -3x) * ln(x + -2) = 0 Reorder the terms: (6 + -3x) * ln(-2 + x) = 0 Reorder the terms for easier multiplication: ln(6 + -3x)(-2 + x) = 0 Multiply (6 + -3x) * (-2 + x) ln(6(-2 + x) + -3x * (-2 + x)) = 0 ln((-2 * 6 + x * 6) + -3x * (-2 + x)) = 0 ln((-12 + 6x) + -3x * (-2 + x)) = 0 ln(-12 + 6x + (-2 * -3x + x * -3x)) = 0 ln(-12 + 6x + (6x + -3x2)) = 0 Combine like terms: 6x + 6x = 12x ln(-12 + 12x + -3x2) = 0 (-12 * ln + 12x * ln + -3x2 * ln) = 0 (-12ln + 12lnx + -3lnx2) = 0 Solving -12ln + 12lnx + -3lnx2 = 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), '3ln'. 3ln(-4 + 4x + -1x2) = 0 Factor a trinomial. 3ln((-2 + x)(2 + -1x)) = 0 Ignore the factor 3.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 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -1x 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 '(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. The solution to this equation could not be determined.
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