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Simplifying 0 = ln(t2 + -6t + 9) Reorder the terms: 0 = ln(9 + -6t + t2) 0 = (9 * ln + -6t * ln + t2 * ln) 0 = (9ln + -6lnt + lnt2) Solving 0 = 9ln + -6lnt + lnt2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 0 + -9ln = 9ln + -6lnt + -9ln + lnt2 Remove the zero: -9ln = 9ln + -6lnt + -9ln + lnt2 Reorder the terms: -9ln = 9ln + -9ln + -6lnt + lnt2 Combine like terms: 9ln + -9ln = 0 -9ln = 0 + -6lnt + lnt2 -9ln = -6lnt + lnt2 Add '6lnt' to each side of the equation. -9ln + 6lnt = -6lnt + 6lnt + lnt2 Combine like terms: -6lnt + 6lnt = 0 -9ln + 6lnt = 0 + lnt2 -9ln + 6lnt = lnt2 Add '-1lnt2' to each side of the equation. -9ln + 6lnt + -1lnt2 = lnt2 + -1lnt2 Combine like terms: lnt2 + -1lnt2 = 0 -9ln + 6lnt + -1lnt2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + 6t + -1t2) = 0 Factor a trinomial. ln((-3 + t)(3 + -1t)) = 0Subproblem 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 '(-3 + t)' equal to zero and attempt to solve: Simplifying -3 + t = 0 Solving -3 + t = 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 + t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0 + 3 t = 0 + 3 Combine like terms: 0 + 3 = 3 t = 3 Add '-1t' to each side of the equation. t + -1t = 3 + -1t Combine like terms: t + -1t = 0 0 = 3 + -1t Simplifying 0 = 3 + -1t 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 '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Add 't' to each side of the equation. -1t + t = -3 + t Combine like terms: -1t + t = 0 0 = -3 + t Simplifying 0 = -3 + t 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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