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Simplifying ln(3x) + -2x2 + 8x + 16 = ln(x + 4) Remove parenthesis around (3x) ln * 3x + -2x2 + 8x + 16 = ln(x + 4) Reorder the terms for easier multiplication: 3ln * x + -2x2 + 8x + 16 = ln(x + 4) Multiply ln * x 3lnx + -2x2 + 8x + 16 = ln(x + 4) Reorder the terms: 16 + 3lnx + 8x + -2x2 = ln(x + 4) Reorder the terms: 16 + 3lnx + 8x + -2x2 = ln(4 + x) 16 + 3lnx + 8x + -2x2 = (4 * ln + x * ln) 16 + 3lnx + 8x + -2x2 = (4ln + lnx) Solving 16 + 3lnx + 8x + -2x2 = 4ln + lnx 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. 16 + 3lnx + 8x + -4ln + -2x2 = 4ln + -4ln + lnx Reorder the terms: 16 + -4ln + 3lnx + 8x + -2x2 = 4ln + -4ln + lnx Combine like terms: 4ln + -4ln = 0 16 + -4ln + 3lnx + 8x + -2x2 = 0 + lnx 16 + -4ln + 3lnx + 8x + -2x2 = lnx Add '-1lnx' to each side of the equation. 16 + -4ln + 3lnx + 8x + -1lnx + -2x2 = lnx + -1lnx Reorder the terms: 16 + -4ln + 3lnx + -1lnx + 8x + -2x2 = lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx 16 + -4ln + 2lnx + 8x + -2x2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 16 + -4ln + 2lnx + 8x + -2x2 = 0 Add '-16' to each side of the equation. 16 + -4ln + 2lnx + 8x + -16 + -2x2 = 0 + -16 Reorder the terms: 16 + -16 + -4ln + 2lnx + 8x + -2x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -4ln + 2lnx + 8x + -2x2 = 0 + -16 -4ln + 2lnx + 8x + -2x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -4ln + 2lnx + 8x + -2x2 = -16 Add '-8x' to each side of the equation. -4ln + 2lnx + 8x + -8x + -2x2 = -16 + -8x Combine like terms: 8x + -8x = 0 -4ln + 2lnx + 0 + -2x2 = -16 + -8x -4ln + 2lnx + -2x2 = -16 + -8x Add '2x2' to each side of the equation. -4ln + 2lnx + -2x2 + 2x2 = -16 + -8x + 2x2 Combine like terms: -2x2 + 2x2 = 0 -4ln + 2lnx + 0 = -16 + -8x + 2x2 -4ln + 2lnx = -16 + -8x + 2x2 Reorder the terms: 16 + -4ln + 2lnx + 8x + -2x2 = -16 + -8x + 2x2 + 16 + 8x + -2x2 Reorder the terms: 16 + -4ln + 2lnx + 8x + -2x2 = -16 + 16 + -8x + 8x + 2x2 + -2x2 Combine like terms: -16 + 16 = 0 16 + -4ln + 2lnx + 8x + -2x2 = 0 + -8x + 8x + 2x2 + -2x2 16 + -4ln + 2lnx + 8x + -2x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 16 + -4ln + 2lnx + 8x + -2x2 = 0 + 2x2 + -2x2 16 + -4ln + 2lnx + 8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 16 + -4ln + 2lnx + 8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -2ln + lnx + 4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -2ln + lnx + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 8 + -2ln + lnx + 4x + -1x2 = 0 Solving 8 + -2ln + lnx + 4x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -2ln + lnx + 4x + -8 + -1x2 = 0 + -8 Reorder the terms: 8 + -8 + -2ln + lnx + 4x + -1x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -2ln + lnx + 4x + -1x2 = 0 + -8 -2ln + lnx + 4x + -1x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -2ln + lnx + 4x + -1x2 = -8 Add '-4x' to each side of the equation. -2ln + lnx + 4x + -4x + -1x2 = -8 + -4x Combine like terms: 4x + -4x = 0 -2ln + lnx + 0 + -1x2 = -8 + -4x -2ln + lnx + -1x2 = -8 + -4x Add 'x2' to each side of the equation. -2ln + lnx + -1x2 + x2 = -8 + -4x + x2 Combine like terms: -1x2 + x2 = 0 -2ln + lnx + 0 = -8 + -4x + x2 -2ln + lnx = -8 + -4x + x2 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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