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Simplifying ln(6x2 + 6x) = ln * 4 Reorder the terms: ln(6x + 6x2) = ln * 4 (6x * ln + 6x2 * ln) = ln * 4 (6lnx + 6lnx2) = ln * 4 Reorder the terms for easier multiplication: 6lnx + 6lnx2 = 4ln Solving 6lnx + 6lnx2 = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 6lnx + -4ln + 6lnx2 = 4ln + -4ln Reorder the terms: -4ln + 6lnx + 6lnx2 = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -4ln + 6lnx + 6lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-2 + 3x + 3x2) = 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 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + 3x + 3x2 = 0 Solving -2 + 3x + 3x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 3x + 2 + 3x2 = 0 + 2 Reorder the terms: -2 + 2 + 3x + 3x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x + 3x2 = 0 + 2 3x + 3x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3x + 3x2 = 2 Add '-3x' to each side of the equation. 3x + -3x + 3x2 = 2 + -3x Combine like terms: 3x + -3x = 0 0 + 3x2 = 2 + -3x 3x2 = 2 + -3x Add '-3x2' to each side of the equation. 3x2 + -3x2 = 2 + -3x + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 = 2 + -3x + -3x2 Simplifying 0 = 2 + -3x + -3x2 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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