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Simplifying ln(6x2 + 11x + 3) + -1(3x + 1) = 5 Reorder the terms: ln(3 + 11x + 6x2) + -1(3x + 1) = 5 (3 * ln + 11x * ln + 6x2 * ln) + -1(3x + 1) = 5 (3ln + 11lnx + 6lnx2) + -1(3x + 1) = 5 Reorder the terms: 3ln + 11lnx + 6lnx2 + -1(1 + 3x) = 5 3ln + 11lnx + 6lnx2 + (1 * -1 + 3x * -1) = 5 3ln + 11lnx + 6lnx2 + (-1 + -3x) = 5 Reorder the terms: -1 + 3ln + 11lnx + 6lnx2 + -3x = 5 Solving -1 + 3ln + 11lnx + 6lnx2 + -3x = 5 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 3ln + 11lnx + 6lnx2 + 1 + -3x = 5 + 1 Reorder the terms: -1 + 1 + 3ln + 11lnx + 6lnx2 + -3x = 5 + 1 Combine like terms: -1 + 1 = 0 0 + 3ln + 11lnx + 6lnx2 + -3x = 5 + 1 3ln + 11lnx + 6lnx2 + -3x = 5 + 1 Combine like terms: 5 + 1 = 6 3ln + 11lnx + 6lnx2 + -3x = 6 Add '3x' to each side of the equation. 3ln + 11lnx + 6lnx2 + -3x + 3x = 6 + 3x Combine like terms: -3x + 3x = 0 3ln + 11lnx + 6lnx2 + 0 = 6 + 3x 3ln + 11lnx + 6lnx2 = 6 + 3x Reorder the terms: -6 + 3ln + 11lnx + 6lnx2 + -3x = 6 + 3x + -6 + -3x Reorder the terms: -6 + 3ln + 11lnx + 6lnx2 + -3x = 6 + -6 + 3x + -3x Combine like terms: 6 + -6 = 0 -6 + 3ln + 11lnx + 6lnx2 + -3x = 0 + 3x + -3x -6 + 3ln + 11lnx + 6lnx2 + -3x = 3x + -3x Combine like terms: 3x + -3x = 0 -6 + 3ln + 11lnx + 6lnx2 + -3x = 0 The solution to this equation could not be determined.
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