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Simplifying (6x + 12) * lnx + -5x + -10 + -16lnx + 8 = 0 Reorder the terms: (12 + 6x) * lnx + -5x + -10 + -16lnx + 8 = 0 Reorder the terms for easier multiplication: lnx(12 + 6x) + -5x + -10 + -16lnx + 8 = 0 (12 * lnx + 6x * lnx) + -5x + -10 + -16lnx + 8 = 0 (12lnx + 6lnx2) + -5x + -10 + -16lnx + 8 = 0 Reorder the terms: -10 + 8 + 12lnx + -16lnx + 6lnx2 + -5x = 0 Combine like terms: -10 + 8 = -2 -2 + 12lnx + -16lnx + 6lnx2 + -5x = 0 Combine like terms: 12lnx + -16lnx = -4lnx -2 + -4lnx + 6lnx2 + -5x = 0 Solving -2 + -4lnx + 6lnx2 + -5x = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -4lnx + 6lnx2 + 2 + -5x = 0 + 2 Reorder the terms: -2 + 2 + -4lnx + 6lnx2 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4lnx + 6lnx2 + -5x = 0 + 2 -4lnx + 6lnx2 + -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -4lnx + 6lnx2 + -5x = 2 Add '5x' to each side of the equation. -4lnx + 6lnx2 + -5x + 5x = 2 + 5x Combine like terms: -5x + 5x = 0 -4lnx + 6lnx2 + 0 = 2 + 5x -4lnx + 6lnx2 = 2 + 5x Reorder the terms: -2 + -4lnx + 6lnx2 + -5x = 2 + 5x + -2 + -5x Reorder the terms: -2 + -4lnx + 6lnx2 + -5x = 2 + -2 + 5x + -5x Combine like terms: 2 + -2 = 0 -2 + -4lnx + 6lnx2 + -5x = 0 + 5x + -5x -2 + -4lnx + 6lnx2 + -5x = 5x + -5x Combine like terms: 5x + -5x = 0 -2 + -4lnx + 6lnx2 + -5x = 0 The solution to this equation could not be determined.
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