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Simplifying (2ln(x) + -16)(4x + -5) = 0 Multiply ln * x (2lnx + -16)(4x + -5) = 0 Reorder the terms: (-16 + 2lnx)(4x + -5) = 0 Reorder the terms: (-16 + 2lnx)(-5 + 4x) = 0 Multiply (-16 + 2lnx) * (-5 + 4x) (-16(-5 + 4x) + 2lnx * (-5 + 4x)) = 0 ((-5 * -16 + 4x * -16) + 2lnx * (-5 + 4x)) = 0 ((80 + -64x) + 2lnx * (-5 + 4x)) = 0 (80 + -64x + (-5 * 2lnx + 4x * 2lnx)) = 0 (80 + -64x + (-10lnx + 8lnx2)) = 0 Reorder the terms: (80 + -10lnx + 8lnx2 + -64x) = 0 (80 + -10lnx + 8lnx2 + -64x) = 0 Solving 80 + -10lnx + 8lnx2 + -64x = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -10lnx + 8lnx2 + -80 + -64x = 0 + -80 Reorder the terms: 80 + -80 + -10lnx + 8lnx2 + -64x = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -10lnx + 8lnx2 + -64x = 0 + -80 -10lnx + 8lnx2 + -64x = 0 + -80 Combine like terms: 0 + -80 = -80 -10lnx + 8lnx2 + -64x = -80 Add '64x' to each side of the equation. -10lnx + 8lnx2 + -64x + 64x = -80 + 64x Combine like terms: -64x + 64x = 0 -10lnx + 8lnx2 + 0 = -80 + 64x -10lnx + 8lnx2 = -80 + 64x Reorder the terms: 80 + -10lnx + 8lnx2 + -64x = -80 + 64x + 80 + -64x Reorder the terms: 80 + -10lnx + 8lnx2 + -64x = -80 + 80 + 64x + -64x Combine like terms: -80 + 80 = 0 80 + -10lnx + 8lnx2 + -64x = 0 + 64x + -64x 80 + -10lnx + 8lnx2 + -64x = 64x + -64x Combine like terms: 64x + -64x = 0 80 + -10lnx + 8lnx2 + -64x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -5lnx + 4lnx2 + -32x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -5lnx + 4lnx2 + -32x)' equal to zero and attempt to solve: Simplifying 40 + -5lnx + 4lnx2 + -32x = 0 Solving 40 + -5lnx + 4lnx2 + -32x = 0 Move all terms containing l to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -5lnx + 4lnx2 + -40 + -32x = 0 + -40 Reorder the terms: 40 + -40 + -5lnx + 4lnx2 + -32x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -5lnx + 4lnx2 + -32x = 0 + -40 -5lnx + 4lnx2 + -32x = 0 + -40 Combine like terms: 0 + -40 = -40 -5lnx + 4lnx2 + -32x = -40 Add '32x' to each side of the equation. -5lnx + 4lnx2 + -32x + 32x = -40 + 32x Combine like terms: -32x + 32x = 0 -5lnx + 4lnx2 + 0 = -40 + 32x -5lnx + 4lnx2 = -40 + 32x 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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