(x^2-4)*ln(3x-6)=0

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Solution for (x^2-4)*ln(3x-6)=0 equation:


Simplifying
(x2 + -4) * ln(3x + -6) = 0

Reorder the terms:
(-4 + x2) * ln(3x + -6) = 0

Reorder the terms:
(-4 + x2) * ln(-6 + 3x) = 0

Reorder the terms for easier multiplication:
ln(-4 + x2)(-6 + 3x) = 0

Multiply (-4 + x2) * (-6 + 3x)
ln(-4(-6 + 3x) + x2(-6 + 3x)) = 0
ln((-6 * -4 + 3x * -4) + x2(-6 + 3x)) = 0
ln((24 + -12x) + x2(-6 + 3x)) = 0
ln(24 + -12x + (-6 * x2 + 3x * x2)) = 0
ln(24 + -12x + (-6x2 + 3x3)) = 0
ln(24 + -12x + -6x2 + 3x3) = 0
(24 * ln + -12x * ln + -6x2 * ln + 3x3 * ln) = 0
(24ln + -12lnx + -6lnx2 + 3lnx3) = 0

Solving
24ln + -12lnx + -6lnx2 + 3lnx3 = 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(8 + -4x + -2x2 + x3) = 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 '(8 + -4x + -2x2 + x3)' equal to zero and attempt to solve: Simplifying 8 + -4x + -2x2 + x3 = 0 Solving 8 + -4x + -2x2 + x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -4x + -2x2 + -8 + x3 = 0 + -8 Reorder the terms: 8 + -8 + -4x + -2x2 + x3 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -4x + -2x2 + x3 = 0 + -8 -4x + -2x2 + x3 = 0 + -8 Combine like terms: 0 + -8 = -8 -4x + -2x2 + x3 = -8 Add '4x' to each side of the equation. -4x + -2x2 + 4x + x3 = -8 + 4x Reorder the terms: -4x + 4x + -2x2 + x3 = -8 + 4x Combine like terms: -4x + 4x = 0 0 + -2x2 + x3 = -8 + 4x -2x2 + x3 = -8 + 4x Add '2x2' to each side of the equation. -2x2 + 2x2 + x3 = -8 + 4x + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + x3 = -8 + 4x + 2x2 x3 = -8 + 4x + 2x2 Add '-1x3' to each side of the equation. x3 + -1x3 = -8 + 4x + 2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = -8 + 4x + 2x2 + -1x3 Simplifying 0 = -8 + 4x + 2x2 + -1x3 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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