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Simplifying 3ln(x + 4) + -6ln(x2 + 7) = 0 Reorder the terms: 3ln(4 + x) + -6ln(x2 + 7) = 0 (4 * 3ln + x * 3ln) + -6ln(x2 + 7) = 0 (12ln + 3lnx) + -6ln(x2 + 7) = 0 Reorder the terms: 12ln + 3lnx + -6ln(7 + x2) = 0 12ln + 3lnx + (7 * -6ln + x2 * -6ln) = 0 12ln + 3lnx + (-42ln + -6lnx2) = 0 Reorder the terms: 12ln + -42ln + 3lnx + -6lnx2 = 0 Combine like terms: 12ln + -42ln = -30ln -30ln + 3lnx + -6lnx2 = 0 Solving -30ln + 3lnx + -6lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-10 + x + -2x2) = 0 Ignore the factor 3.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 '(-10 + x + -2x2)' equal to zero and attempt to solve: Simplifying -10 + x + -2x2 = 0 Solving -10 + x + -2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + x + 10 + -2x2 = 0 + 10 Reorder the terms: -10 + 10 + x + -2x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x + -2x2 = 0 + 10 x + -2x2 = 0 + 10 Combine like terms: 0 + 10 = 10 x + -2x2 = 10 Add '-1x' to each side of the equation. x + -1x + -2x2 = 10 + -1x Combine like terms: x + -1x = 0 0 + -2x2 = 10 + -1x -2x2 = 10 + -1x Add '2x2' to each side of the equation. -2x2 + 2x2 = 10 + -1x + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 = 10 + -1x + 2x2 Simplifying 0 = 10 + -1x + 2x2 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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