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Simplifying ln(4x2 + 7x + -15) + -1ln(4x + -5) = 0 Reorder the terms: ln(-15 + 7x + 4x2) + -1ln(4x + -5) = 0 (-15 * ln + 7x * ln + 4x2 * ln) + -1ln(4x + -5) = 0 (-15ln + 7lnx + 4lnx2) + -1ln(4x + -5) = 0 Reorder the terms: -15ln + 7lnx + 4lnx2 + -1ln(-5 + 4x) = 0 -15ln + 7lnx + 4lnx2 + (-5 * -1ln + 4x * -1ln) = 0 -15ln + 7lnx + 4lnx2 + (5ln + -4lnx) = 0 Reorder the terms: -15ln + 5ln + 7lnx + -4lnx + 4lnx2 = 0 Combine like terms: -15ln + 5ln = -10ln -10ln + 7lnx + -4lnx + 4lnx2 = 0 Combine like terms: 7lnx + -4lnx = 3lnx -10ln + 3lnx + 4lnx2 = 0 Solving -10ln + 3lnx + 4lnx2 = 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), 'ln'. ln(-10 + 3x + 4x2) = 0 Factor a trinomial. ln((-2 + -1x)(5 + -4x)) = 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 '(-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 '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Add '4x' to each side of the equation. -4x + 4x = -5 + 4x Combine like terms: -4x + 4x = 0 0 = -5 + 4x Simplifying 0 = -5 + 4x 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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