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Simplifying (y + 4) * ln(2y + 3) = 0 Reorder the terms: (4 + y) * ln(2y + 3) = 0 Reorder the terms: (4 + y) * ln(3 + 2y) = 0 Reorder the terms for easier multiplication: ln(4 + y)(3 + 2y) = 0 Multiply (4 + y) * (3 + 2y) ln(4(3 + 2y) + y(3 + 2y)) = 0 ln((3 * 4 + 2y * 4) + y(3 + 2y)) = 0 ln((12 + 8y) + y(3 + 2y)) = 0 ln(12 + 8y + (3 * y + 2y * y)) = 0 ln(12 + 8y + (3y + 2y2)) = 0 Combine like terms: 8y + 3y = 11y ln(12 + 11y + 2y2) = 0 (12 * ln + 11y * ln + 2y2 * ln) = 0 (12ln + 11lny + 2lny2) = 0 Solving 12ln + 11lny + 2lny2 = 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(12 + 11y + 2y2) = 0 Factor a trinomial. ln((4 + y)(3 + 2y)) = 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 '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 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 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Add '-1y' to each side of the equation. y + -1y = -4 + -1y Combine like terms: y + -1y = 0 0 = -4 + -1y Simplifying 0 = -4 + -1y 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 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 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 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Add '-2y' to each side of the equation. 2y + -2y = -3 + -2y Combine like terms: 2y + -2y = 0 0 = -3 + -2y Simplifying 0 = -3 + -2y 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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